Final answer:
There are 24 different 5-card poker hands containing 3 aces and 2 kings possible from a standard 52-card deck, calculated by multiplying the number of combinations of aces and kings.
Step-by-step explanation:
To determine how many 5-card poker hands consisting of 3 aces and 2 kings are possible from an ordinary 52-card deck, we need to use combinations. A combination is a selection of items without regard to order.
There are 4 aces in a deck and we need to choose 3 of them. The number of ways to do this is given by the combination formula C(4,3). Similarly, there are also 4 kings in a deck and we need 2 of them, so we use C(4,2) to find out how many ways we can select the kings.
The total number of 5-card poker hands with 3 aces and 2 kings is given by multiplying these two combinations:
C(4,3) = 4 (since there are 4 ways to leave out one ace)
C(4,2) = 6 (since there are 6 ways to pick 2 kings out of 4)
So, the total number of hands possible is 4 * 6 = 24.
Therefore, there are 24 different 5-card poker hands with 3 aces and 2 kings possible in a standard deck of 52 cards.