Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of differentpoker hands of the specified type.two pairs (two of one denomination, two of another denomination, and one of a third)For those unfamiliar with playing cards, here is a short description. A standard deck consists of 52 playingcards. Each card is in one of 13 denominations: ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), queen (Q), andking (K), and in one of four suits: hearts (V), diamonds (), clubs (), and spades (). Thus, forinstance, the jack of spades, J, refers to the denomination of jack in the suit of spades. The entire deck ofcards is as shown below.AV 20 3V 4V 5V 60 7♥ 8♥ 9♥ 10♥ JV Q♥ _K♥6+ 7+ 8+ 9+ 10+ J+ Q• K•A* 24 34 44 54 64 74 84 94 104 JA Q4 KAJA Q4 KAA2+ 3+ 4+ 5+A424 3444 5474 8494104Step 1Recall that the entire deck of cards is as follows.10 JV Q♥ K♥J• Q• K•A* 24 34 44 54 64 74 84 94 104 JA Q4 KA104 JA Q4 KAAV 2v 3V 4♥ 5V 6♥ 7♥ 8♥ 9♥A2. 3+4+ 5+6. 7+ 8• 94 10+A+24 344454 6474 84 94The goal is to determine the number of different five-card poker hands that consists of two pairs. In otherwords, we need to find the number of ways to pick 2 cards of one denomination, 2 cards of anotherdenomination, and a final card that belongs to neither of the first two denominations.Our decision algorithm is a sequence of four steps.Step 1: Select 2 denominations for the pairs.Step 2: Select 2 cards from one selected denomination.Step 3: Select 2 cards from the other selected denomination.Step 4: Select 1 card that belongs to neither of the previously selected denominations.We begin with Step 1. There are 13 possible denominations and we will pick 2 of them. Because the order thatwe make this selection does not matter, we will use combinations to find the number of ways to pick 2denominations out of 13.Therefore, in each case we will be using combinations to count the number of ways to take n items taken r ata time, which is calculated using the following formula.n!C(n, r) =rl(n - r)!Here we haven = 13 and r = 2. Substitute these values into the formula and simplify.nlC(n, r) =rl(n - r)!13 V13 !C(13, 2) =2!(13 - 2)!7878In other words, there are 78 v78 possible ways to pick 2 of the 13 denominations for the pairs.Step 2We now move on to Steps 2 and 3.Step 1: Select 2 denominations for the pairs (78 possible ways).Step 2: Select 2 cards from one selected denomination.Step 3: Select 2 cards from the other selected denomination.Step 4: Select 1 card that belongs to neither of the previously selected denominations.| cards of each denomination.ways to pick 2 cards from one of the selectedThe two denominations have now been selected. There areTherefore, there are Cdenominations.Similarly, there are alsoways to pick 2 cards from the other selected denomination.

Name: Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: Tutorial ExercisePoker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of differentpoker hands of the specified type.two pairs (two of one denomination, two of another denomination, and one of a third)For those unf

Question

Accepted Answer

Step 2 of the problem:
Since there are 4 cards of each denomination; therefore, there are C24=6 ways…

Poker Hands A poker hand consists of 5 cards from a standard deck of 52. Find the number of different poker hands of the specified type. two pairs (two of one denomination, two of another denomination, and one of a third)