How many 5 card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 52-card deck?

Answer choice: a).12 b).288 c).6 d).24

I got 24 is that correct?

Number of possible 3-ace combinations = 4. Number of possible 2-kings combinations = 4!/2!2! = 6.

The answer is the product, which is 24.

To determine the number of 5-card poker hands consisting of 3 aces and 2 kings, we can break it down into two steps:

Step 1: Selecting the 3 aces
There are 4 aces in a standard deck of 52 cards, so we need to choose 3 of them. The number of ways to do this is given by the combination formula:

C(4, 3) = 4! / (3!(4-3)!) = 4

Step 2: Selecting the 2 kings
Similarly, there are 4 kings in a standard deck of 52 cards, and we need to choose 2 of them:

C(4, 2) = 4! / (2!(4-2)!) = 6

Finally, we calculate the total number of 5-card poker hands by multiplying the results from step 1 and step 2 together:

Total = 4 * 6 = 24

Therefore, your answer of 24 is correct.

To determine the number of 5-card poker hands consisting of 3 aces and 2 kings, we can break down the problem into two steps:

Step 1: Calculate the number of ways to choose 3 aces from a deck of 4 aces.
Since there are 4 aces in a deck, and we need to select 3 of them, we can use the combination formula. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of elements, and r is the number of elements to select.

In this case, we have n = 4 aces and r = 3.
So, the number of ways to choose 3 aces from 4 aces is 4C3 = 4! / (3!(4-3)!) = 4.

Step 2: Calculate the number of ways to choose 2 kings from a deck of 4 kings.
Similarly, there are 4 kings in a deck, and we need to select 2 of them.
So, the number of ways to choose 2 kings from 4 kings is 4C2 = 4! / (2!(4-2)!) = 6.

Finally, we multiply the results of both steps together to find the total number of 5-card poker hands consisting of 3 aces and 2 kings:
Total = Number of ways to choose 3 aces × Number of ways to choose 2 kings
Total = 4 × 6 = 24

Therefore, the correct answer is d). 24.

So, your answer of 24 is correct.