The goal is to determine the number of different five-card poker hands that consists of two pairs. In other words, we need to find the number of ways to pick 2 cards of one denomination, 2 cards of another denomination, 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 that we make this selection does not matter, we will use combinations to find the number of ways to pick 2 denominations out of 13. Therefore, in each case we will be using combinations to count the number of ways to take n items taken r at a time, which is calculated using the following formula. n! C(n, r) = r!(n - r)! Here we have n = 13 andr= 2. Substitute these values into the formula and simplify. n! C(n, r) = r!(n r)! C(13, 2) = 2!(13 – 2)! In other words, there are possible ways to pick 2 of the 13 denominations for the pairs.
The goal is to determine the number of different five-card poker hands that consists of two pairs. In other words, we need to find the number of ways to pick 2 cards of one denomination, 2 cards of another denomination, 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 that we make this selection does not matter, we will use combinations to find the number of ways to pick 2 denominations out of 13. Therefore, in each case we will be using combinations to count the number of ways to take n items taken r at a time, which is calculated using the following formula. n! C(n, r) = r!(n - r)! Here we have n = 13 andr= 2. Substitute these values into the formula and simplify. n! C(n, r) = r!(n r)! C(13, 2) = 2!(13 – 2)! In other words, there are possible ways to pick 2 of the 13 denominations for the pairs.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 81E: Hockey Lineup A hockey team has 20 players, of whom 12 play forward, six play defense, and two are...
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