In how many ways can a full house of three jacks and a pair of twos be obtained from an ordinary deck of cards?
c(4,2) = 6 so that the final answer is 4*6 = 24 not 12
To determine the number of ways a full house of three jacks and a pair of twos can be obtained from an ordinary deck of cards, we need to calculate the combinations.
Step 1: Calculate the number of ways to choose 3 jacks from the 4 available.
The number of ways to choose 3 jacks from 4 jacks is given by the combination formula:
C(4, 3) = 4! / (3! * (4-3)!) = 4
Step 2: Calculate the number of ways to choose 2 twos from the 4 available.
The number of ways to choose 2 twos from 4 twos is also given by the combination formula:
C(4, 2) = 4! / (2! * (4-2)!) = 6
Step 3: Calculate the total number of ways to obtain a full house of three jacks and a pair of twos. Since you need to have exactly 3 jacks and 2 twos, we multiply the number of ways calculated in Step 1 and Step 2:
Total number of ways = C(4, 3) * C(4, 2) = 4 * 6 = 24
Therefore, there are 24 ways to obtain a full house with three jacks and a pair of twos from an ordinary deck of cards.
To find the number of ways to obtain a full house of three jacks and a pair of twos from a standard deck of cards, we need to break down the problem.
A full house consists of three cards of the same rank and two cards of another rank. In this case, we want three jacks and two twos. There are four jacks and four twos in a deck of cards.
Let's calculate the number of ways to select three jacks from four and two twos from four:
First, we choose the three jacks:
There are four jacks in total, and we need to select three.
The number of ways to select three jacks from four is calculated using the combination formula: C(n, r) = n! / (r! * (n-r)!)
In this case, C(4, 3) equals 4! / (3! * (4-3)!) = 4.
Next, we choose the two twos:
There are four twos in total, and we need to select two.
Using the same combination formula, C(4, 2) equals 4! / (2! * (4-2)!) = 6.
To obtain a full house, we need to multiply the number of ways to select three jacks by the number of ways to select two twos:
4 * 6 = 24.
Therefore, there are 24 ways to obtain a full house of three jacks and a pair of twos from an ordinary deck of cards.
combination of 4 jacks 3 at a time
C(4,3) = 4! /[ 3! (4-3)! ] = 4
combination of 4 twos 2 at a time
c(4,2) = 4! /[2!(4-2)!] = 3
so
4*3 = 12