Note that each number in the triangle other than the 1's at the ends of each row is the sum of the two numbers to the right and left of it in the row above. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king? Advertisement. View solution >1. Solution For Determine the number of 5-card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. The 5 cards of the hand are all distinct, and the order of cards in the hand does not matter so it is a combinatorial problem. Solution: Given a deck of 52 cards. There are 52 cards in a poker deck, and a hand is a combination of 5 of those cards. Frequency is the number of ways to draw the hand, including the same card values in different suits. View Solution. . 1 answer. So the formula for a permutation of k items out of n items [notation for a Permutation is n_P_k]is n!/(n-k)!1 Expert Answer. This is called the number of combinations of n taken k at a time, which is sometimes written . Generate all possible combinations of. The following exercises deal with our version of the game blackjack. However, there is a "natural" sample space, the set of $5$-card hands, and we will work with that. There are displaystyle 3!=3cdot 2cdot 1=6 3! = 3 ⋅ 2 ⋅ 1 = 6 ways to order 3 paintings. View solution >We can use combinations to calculate the probability of selecting certain arrangements of objects. Answer. Find the total number of possible five-card poker hands. Calculate the probability of success raised to the power of the number of successes that are px. To find the total number of outcomes for two or more events, multiply the number of outcomes for each event together. Containing four of a kind, that is, four cards of the same denomination. Combinatorial calculator - calculates the number of options (combinations, variations. The following table shows the number of combinations for 2 to 10 cards from a single 52-card deck, with no wild cards. The remaining percentage consists. Question: Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Practice Problem: There are five remaining cards from a standard deck. There are $24$ such cards. If you want to count the size of the complement set and subtract off from ${52 choose 5}$, then you need to find the number of five card poker hands which contain one or more cards of another suite. View Solution. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. The game is played with a pack containing 52 cards in 4 suits, consisting of: 13 hearts: 13 diamonds. How many different hands can he draw? Solution: This problem requires us to calculate the number of combinations of five cards taken two at a time. Subtract the numerator (5) from the denominator (13) : 13 - 5 = 8 . Approximately 50% of "poker hands”, a set of 5 cards, have no pair or other special combination of cards, approximately 42% of hands have exactly one pair of same valued cards, and only 2. The number of combinations n=10, k=4 is 210 - calculation result using a combinatorial calculator. Of these 56 combinations, there are 3Cl × 2Cl × 3Cl = 18 combinations consisting of one red, one white, and one blue. (Total 5-card combinations) = [(C(13, 5) * 4) – (10 * 4)] / C(52, 5) This probability, though involving some calculations, is approximately 0. We assume that we can see the next five cards (they are not hidden). For example, we can take out any combination of 2 cards. 05:26. You are "duplicating combinations", because the same king that you choose out of 4 4 kings in one combination, can be chosen out of 51 51 cards in another combination. From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king. four of the same suit. Click here👆to get an answer to your question ️ Determine the number of 5 - card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. So, the total number of combinations is $4 imes C(48, 4) =. ∴ The number of ways to select 1 Ace from 4 Ace cards is 4 C 1Each of these 20 different possible selections is called a permutation. A. There are total 4 aces in the deck of 52 cards. The highest card in a straight can be 5,6,7,8,9,10,Jack,Queen,King, or Ace. asked Dec 30, 2016 in Mathematics by sforrest072 ( 130k points) permutations and combinations In a deck, there is 4 ace out of 52 cards. Find the number of 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination. A. The concepts you are looking for are known as "permutations" and "combinations. 05:26. Q. Write combination or permutation on the space provided. Solution. 2. Things You Should Know. Each combination of 3 balls can represent 3! different permutations. Mathematics Combination with Restrictions Determine the. Then, one ace can be selected in `""^4C_1` ways and the remaining 4 cards can be selected out of the 48 cards in `"^48C_4`ways. Combinations sound simpler than permutations, and they are. Given a deck of $52$ cards. Determine the number of 5 cards combination out of a deck of 52 cards if at least one of the cards has to be a king. Here we have a set with n n elements, e. How many different astrological configurations are possible for n = 100? There are 20 rabbits, 15. A poker hand consists of 5 cards randomly drawn from a deck of 52 cards. ⇒ 778320. (A poker hand consists of 5 cards dealt in any order. Transcript. 2! × 9! = 55. A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. statistics. In a pack of 52 cards , there are four aces. One card is selected from a deck of playing cards. A combination of 5 cards have to be made in which there is exactly one ace. Determine the number of 5 card combination out of a deck of 5 2 cards if each selection of 5 cards has at least one king. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. Click on Go, then wait for combinations to load. 7 to 1: Combinations 54,912: Three of a Kind is three of one card and. In this example, you should have 24 * 720, so 17,280 will be your denominator. In the standard game of poker, each player gets 5 cards and places a bet, hoping his cards are "better" than the other players' hands. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. $$mathsf P(Kleq 3) = 1 -mathsf P(K=4)$$ The probability that you will have exactly all four kings is the count of ways to select 4 kings and 1 other card divided by the count of ways to select any 5 cards. Ex 6. IIT-JEE. This function takes two arguments: the number and the number_chosen. Statistics and probability 16 units · 157 skills. In a deck of 52 cards, there are 4 aces. In a card game, order does not matter, making this a combination and not a permutation. We assume that we can see the next five cards (they are not hidden). There are total 4 King Cards out of 52 We have to select 1 King from 4 King cards The Remaining 4 we have to select from 48 cards (52 − 4 king cards) Total number of ways = 4C1 × 48C4 = 4!/1!(4 − 1)! × 48!/4!(48 − 4)! We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula n Cᵣ = n! / [r!(n−r)!]. You can also convert the probability into a percentage by multiplying it by 100. 6 Exercises. Determine the number of 5 card combination out of deck of 52 cards if there is exactly one ace in each combination. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. Try hash = index % prime * 52 * 52 * 52 + index to even out the distribution. Calculate the number of different 5-card poker hands that make a full house - 3 of a kind plus a pair. We are given 10 cards, the first 5 are the current hand, and the second 5 are the next five cards in the deck. Probability of getting a hand that has 5 cards of the same suit (flush, straight flush, royal flush) =5148/2598960~=. In this card game, players are dealt a hand of two cards from a standard deck. 3k points) Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. 1 king can be selected out of 4. The number of ordered arrangements of r objects taken from n unlike objects is: n P r = n! . However, since suits are interchangeable in poker, many of these are equivalent - the hand 2H 2C 3H 3S 4D is equivalent to 2D 2S 3D 3C 4H - simply swap the suits around. You can calculate it using the formula C(n,r) = n! / [r!(n-r)!], where 'n' is the number of items to choose from (52 cards in. Thus a flush is a combination of five cards from a total of 13 of the same suit. For example, count the number of five-card combinations that can be classified as a straight flush. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Find how many combinations of : 3 cards of equal face values and 2 cards of different values. A combination of 5 cards have to be made in which there is exactly one ace. The answer is the binomial coefficient (26 C 5) and you can read this as 26 choose 5. A class has to elect 3 members of a committee from 6 candidates. 05:01. Use the formula for calculating combinations: C(n, r) = (n!) / [(r!) x (n - r)!] Then follow these four steps to calculate how many combinations you can obtain from a sample set: 1. Thus, the number of combinations is:asked Sep 5, 2018 in Mathematics by Sagarmatha (55. He has 5 jackets, 4 pairs of shoes, 3 pairs of pants, 2 suitcases and a carry bag. $ Section 7. The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. We count the number of $5$-card hands that have exactly $1$ card below $8$. Now for each of the $5$ cards we have $4$ choices for the suit, giving a total of $(10)(4^5)$. ISBN: 9781938168383. Note: You might think why we have multiplied the selection of an ace card with non ace cards. it should be in a particular order. The total number of combinations would be 2^7 = 128. Since there are 52 cards in a deck and the order of cards doesn’t matter, the sample space for this experiment has 52 C 5 = 2,598, 960 52 C 5 = 2,598,960 possible 5-card hands. Note that the cumulative column contains the probability of being dealt that hand or any of. Full house. Combinations Worksheet Name Assig e Determine whether each situation involves a permutation or a combination. Thus, we have 6840 and 2380 possible groupings. 00198. There are 52 13 = 39 cards that North does not hold. ⇒ C 1 4 × C 4 48. Thus there are $(10)(4^5)-40$ straights. There are 40 cards eligible to be the smallest card in a straight flush. In 5-Card combinations, you would have 4 possible royal flushes. This value is always. _square]. Generate all possible combinations of. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. View Solution. Core combo: Citi Double Cash® Card and Citi Premier® Card. Best Citi credit card combo. 05:12. 2. 1 king can be selected out of 4 kings in `""^4C_1` ways. Combinatorics is a fancy term for evaluating the number of possible “combinations” (combos) of any given hand: the combination of 2 cards of certain ranks and suits. 2. Click here👆to get an answer to your question ️ "the strip. Lastly, we multiply those two quantities to get the probability of drawing 4 cards with 2 aces and 2 kings regardless of arrangement. Determine the number of 5 -card combination out of a deck of 52 cards if each selection of 5 cards has exactly one king. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Verified by Toppr. So of those nearly 2. Draw new cards to replace the ones you don't want to keep, then fold or bet again. In Combinations ABC is the same as ACB because you are combining the same letters (or people). When we need to compute probabilities, we often need to multiple descending numbers. Your $\dfrac{52!}{47!}$ is the number of ways to deal $5$ cards: it counts each of the $5!=120$ possible dealing orders of a given hand separately. a) Three face cards, b) A heart flush (all hearts). . 144 %. taken from a standard 52 card deck? (using combinations)-----# of possible 5-card hands: 52C5 # of 5-card hands with no kings: 48C5-----Ans: 52C5-48C5 = 2,404,380 ===== Find the number of possible 5 card hands that contain At Most 1 diamond. No. From the introduction, the number of sets is just: \[52\times51\times50\times49\times48 onumber \] Determine the number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination. The probability that an adult possesses a credit card is 0. n } and we want to draw k k samples from the set such that ordering does not matter and repetition is not allowed. The other way is to manually derive this number by realizing that to make a high card hand the hand must consist of all five cards being unpaired, non-sequential in rank, and not all of the same suit. 8. of ways of selecting 4 cards from the remaining deck of 48 cards = ⁴⁸C₄. The number of ways to choose 5 cards from the 13 cards which are diamonds is ${13 choose 5}$. How many distinct poker hands could be dealt?. Thus, the number of combinations is: 52 C 5 = 52! / 5!(52 - 5)! or 52! / 5!47! = 2,598,960. Then, one ace can be selected in 4 C 1 ways and the remaining 4 cards can be selected out of the 4 8 cards in 4 8 C 4 ways. Question: 2. The formula for nCx is where n! = n(n-1)(n-2) . Misc 8 Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. You also know how many have no kings. 1 king can be selected out of 4 kings in `""^4C_1` ways. The 11 Best Credit Card Combinations – Amex, Chase, Citi, Capital One [November 2023] Stephen Au Updated: November 14, 2023, 12:59pm CST. With well formed sets not every index is reachable and the distribution is skewed towards lower numbers. Explanation: To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. (e. Example: Combination #2. Courses. How many ordered samples of 5 cards can be drawn from a deck of 52. The Probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand ( Frequency) by the total number of 5-card hands (the sample space; ( 52 5 ) = 2 , 598 , 960 { extstyle {52 choose 5}=2,598,960}So we say that there are 5 factorial = 5! = 5x4x3x2x1 = 120 ways to arrange five objects. Then, one ace can be selected in ways and other 4 cards can be selected in ways. Determine the number of five-card poker hands that can be dealt from a deck of 52 cards. Determine the number of 5. these 16 cards, 4 are chosen. A combination of 5 cards have to be made in which there is exactly one ace. For the 3 cards you have 52 × 3. Click here👆to get an answer to your question ️ "the strip. 48 C 2 = (48 x 47)/(2 x 1) = 1128 ways. In a deck of 52 cards, there are 4 kings. This probability is. In this case, you are looking for a permutation of the number of ways to order 5 cards from a set of 52 objects. Number of cards in a deck = 52. We refer to this as a permutation of 6 taken 3 at a time. (c) a hand of cards in poker. In order to find the actual number of choices we take the number of possible permutations and divide by 6 to arrive at the actual answer: 7C3 = 7P3 3! = 7! 4! ∗ 3! In a combination in which the order is not. asked Apr 30, 2020 in Permutations and Combinations by PritiKumari ( 49. The number of ways to choose 5 cards from the 13 cards which are diamonds is ${13 choose 5}$. ∴ No. Chemical KineticsMoving Charges and MagnetismMicrobes in Human WelfareSemiconductor Electronics: Materials, Devices and Simple Circuits. View Solution. Therefore, to calculate the number of combinations of 3 people (or letters) from a set of six, you need to divide 6! by 3!. Then a comma and a list of items separated by commas. Again for the curious, the equation for combinations with replacement is provided below: n C r =. CBSE Board. 0k points) combinations; class-11; 0 votes. Q5. We need to calculate how many unique combinations we can make. Step by step video, text & image solution for Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. We need to select exactly one ace for our combination. P (None blue) There are 5 non-blue marbles, therefore. There are also two types of combinations (remember the order does not matter now): Repetition is Allowed: such as coins in your pocket (5,5,5,10,10) No Repetition: such as lottery numbers (2,14,15,27,30,33) 1. ADVERTISEMENT. A standard deck of cards has 12 face cards and four Aces (Aces are; Suppose you have a standard deck 52 cards (4 suits: hearts, diamonds, clubs, and spades. P (ace, ace, king, king) ⋅ ₄C₂ = 36 / 270725. For a straight flush this is easy, just look at the highest card in the hand, find the difference between it and 13 (where J=11, Q=12, K=13), multiply that by 4, and add 5 (the starting point for straight flushes). Solve Study Textbooks Guides. If we sum the preceding numbers, we obtain 2,598,960 and we can be confident the numbers are correct. Order doesn't matter, because A,2,3,4,5 is the same hand has 3,4,2,A,5. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. What is the probability that the number on the ball is divisible by 2 or 3. The index part added ensures the hash will remain unique. 1% of hands have three of a kind. We can calculate the number of outcomes for any given choice using the fundamental counting principle. My (incorrect) logic was that there are 13. To consider straights independently from straight flushes, remove the 4 possible straight flushes from each of the 10 initial positions, giving you $(4^5-4)*10$. combination is possible. 2 Answers Lotusbluete Feb 2, 2016 There are #10# possible #5#-card hands with exactly #3# kings and exactly #2# aces. of cards in a deck of cards = 52. How many possible 5 card hands from a standard 52 card deck would consist of the following cards? (a) two clubs and three non-clubs (b) four face cards and one non-face card (c) three red cards, one club, and one spade (a) There are five-card hands consisting of two clubs and three non-clubs. Below, we calculate the probability of each of the. Solve Study Textbooks Guides. In a 5 card poker with a standard 52- card deck, 2, 598, 960 different hands are possible. If there is exactly one ace in each 5 card combination, then one ace out of 4 can be selected in 4 C 1 ways and 4 non-ace cards can be selected out of 48 in 48 C 4 ways. 1-on-1 Online Tutoring. In This Article. It makes sense that there are fewer choices for a combination than a permutation, since the redundancies are being removed. Player 1's Best Hand is: A A Q Q 8 8 6 6 5 5. This is the total number of arrangements of 2 Aces of the 4 in A. This approach indicates that there are 10 possible combinations of 5 cards taken 2 at a time. Determine the number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination. 7. Q3. There are 13 2 di erent ways to choose 2 denominations from the 13 available denominations. A flush consists of five cards which are all of the same suit. Cards are dealt in. What is the probability that the number on the ball is divisible by 2 or 3. (f) an automobile license plate. ,89; 3. g. That equals 290,700. An example is 9♥, 8♣, 7♠, 6♦, 5♥. View Solution. Lastly, we multiply those two quantities to get the probability of drawing 4 cards with 2 aces and 2 kings regardless of arrangement. magic filters photo_filter. We want to exchange any n number of cards (where n <= 5) in our hand for the next n cards in the deck. n C r = n! ⁄ r! (n-r)! ,0 < r ≤n. Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king ? Q. . 02:15. Since there are four different suits, there are a total of 4 x 1287 = 5148. 13 clubs:To determine the number of combinations, simply divide the number of permutations by the factorial of the size of the subset. - 36! is the number of ways 36 cards can be arranged. All we care is which five cards can be found in a hand. e. 1 / 4. 000154%In a deck of 52 cards, there are 4 aces. 13 × 1 × 48 13 × 1 × 48. 7) How many ways can the positions of president and vice president be assigned from a group of 8 people? 8) Find the Number of hugs possible in a family of 5 people (no repeat hugs). ∴ The number of ways to select 1 Ace from 4 Ace cards is 4 C 1Each of these 20 different possible selections is called a permutation. 28. (a) a telephone number. Solution. Since in the combination of 5 cards, one place is occupied by a king, thus there remain 4 cards and also the total number of cards left is 48 after the removal of 4 kings from 52 cards. Permutation: Listing your 3 favorite desserts, in order, from a menu of 10. We are given 10 cards, the first 5 are the current hand, and the second 5 are the next five cards in the deck. There are 52 cards in a poker deck, and a hand is a combination of 5 of those cards. It may take a while to generate large number of combinations. From a standard 52-card deck, how many 5-card hands consist entirely of red cards? Solution: There are total 26 red card i. In a deck of 52 cards, there are 4 kings. one can compute the number of. Where: Advertisement. 5 card poker hand combination a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter n P r = n!/r!(n - r)! factorial The product of an integer and all the integers below it probability the likelihood of an event happening. 2. counts each hand based upon the number of ways you can arrange five cards. One king from 4 kings can be selected in- ^prime, ways and 4 cards from 48 cards can be . A royal flush is defined as an ace-high straight flush. Part a) is effectively asking, given these 39 cards how many ways are there of choosing 5 in other words what is 39 choose 5: $$inom{39}{5}=575757$$ For part b) we can do something similar, lets start with choosing 1 club. I developed a simulator Texas hold'em and during this development I found the number of 7462 unique combinations (52 - 5/5 cards) on the flop. This value is always. Find the number of 5-card combinations out of a deck of 52 cards if a least one of the five cards has to be king. There are 2,598,960 ways to choose 5 cards out of a 52-card deck. Click on Go, then wait for combinations to load. Class 9. Thus, we basically want to choose a k k -element subset of A A, which we also call a k. 71. Thus the number of ways of selecting the cards is the combination of 48 cards taken 4 at a time. IIT-JEE. We are using the principle that N (5 card hands)=N. West gets 13 of those cards. Sorted by: 1. Image/Mathematical drawings are created in Geogebra. Three of a Kind – This combination contains three cards of the same rank, and the other two cards each of a different rank, such as. We may be compensated when you click on product links, such as credit cards, from one or more of our advertising partners. **two pairs with exactly one pair being aces (two aces, two of another denomination, and one of a third)**. Divide the latter by the former. B. Theorem 2. In general we say that there are n! permutations of n objects. 2. There are 13 values you can select for the four of a kind: ${13 choose 1}$ The fifth can be any of the 52 - 4 remaining cards: ${52 - 4 choose 1}$For each condition, you can have two possibilities: True or False. So in this case, you can simply get the answer without using any formulas: xy, xz, yz, xyz x y, x z, y z, x y z. A straight flush is completely determined once the smallest card in the straight flush is known. F F. Click the card to flip 👆. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king Solution: The total no. The "proof" is that they are selecting three cards from 26 black ones, and then picking 2 from the remaining. Click here👆to get an answer to your question ️ \"Determine the number of 5 - card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Create Tests & Flashcards. To convert the number of combinations or permutations into a probability of drawing a specific results, divide one by the result of your calculation. The total number of possible choices is 52 × 51 × 50 × 49 × 48 52 × 51 × 50 × 49 × 48. )Refer to Example 9. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Open in App. In computer security, if you want to estimate how strong a password is based on the computing power required to brute force it, you calculate the number of permutations, not the number of combinations. Answers 2. #combination #permutation #maths #lecture Determine the number of 5 card combination out of 52 cards if there is exactly one ace in each combinationFind the. Selection of 5 cards having at least one king can be made as follows: 1 king and 4 non kings or 2 kings and 3 non kings or 3 kings and 2 non kings or 4 kings and 1 non king. P (full house) = 3744 2,598,960 ≅. View Solution. Statistics Probability Combinations and Permutations. Combination State if each scenario involves a permutation or a combination. In a deck of 52 cards, there are 4 kings. Q2. Question . The observation that in a deck of 52 cards we have 4 kings and 48 non kings. 2: The Binomial Theorem. For the purpose of this table, a royal flush, straight flush, flush, and straight must use all cards. From a deck of 52 cards, 5 cards combination is taken out Find the number of combinations at which the combination has at least one ace. Combination Formulas. Ex 6. 4, 6 Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in. Here are the steps to follow when using this combination formula calculator: On the left side, enter the values for the Number of Objects (n) and the Sample Size (r). r-combinations of a set with n distinct elements is denoted by . Solve Study Textbooks Guides. asked Sep 5, 2018 in Mathematics by Sagarmatha ( 55. So you want to stick with $4^5*10$ in your numerator. Determine the probability of selecting: a card greater than 9 or a black card. This probability is. In case two or more players have the same high pair, the tie is broken by. 144% To find the probability of finding a full house (a three of a kind and a 2 of a kind in the same 5-card hand), we find the number of ways we can achieve the full house and divide by the number of 5. The answer is the number of unfavorable outcomes. Example 2: If you play a standard bingo game (numbers from 1 to 75) and you have 25 players (25 cards), and if you play 30 random values, you will get an average of 3 winning lines. c) Two hearts and three diamonds. Straight – Five cards in sequence, but not all of the same suit is a straight. Then your index is simply card1 + 52 * card2 + 52 * 52 * card3. taken from a standard 52 card. When you draw five numbers out of 69 without repetition, there are 11,238,513 combinations. And we want to arrange them in unordered groups of 5, so r = 5. Number of kings =4 . Answer: The number of 3-letter words that can be formed by using the letters of the word says, HELLO; 5 P 3 = 5!/(5-3)! this is an example of a permutation. You randomly draw cards from a standard deck of playing cards and place them face up on the table. I. 00196 To find the probability, we need to find the fraction where the numerator is the number of ways to have a flush and the. 2! × 9! = 55. The answer is \(\binom{52}{5}\). difference between your two methods is about "how" you select your cards. .