Question

How many five-card poker hands containing exactly three aces are possible?

Answer 1

The number of five-card poker hands containing exactly three aces is 4,512.

Step-by-step explanation:

To find the number of five-card poker hands containing exactly three aces, we need to calculate the combination of choosing 3 aces from a deck of 4 aces, multiplied by the combination of choosing 2 cards from the remaining 48 cards in the deck. The formula for combination is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen.

The combination of choosing 3 aces from 4 is: 4C3 = 4! / (3!(4-3)!) = 4

The combination of choosing 2 cards from the remaining 48 is: 48C2 = 48! / (2!(48-2)!) = 1,128

Therefore, the number of five-card poker hands containing exactly three aces is: 4 * 1,128 = 4,512

Answer 2

3 aces and 2 other cards: AAA??

There are 4 possible aces and 48 possible non-aces

AAA = 4 x 3 x 2 ?? = 48 x 47

AAA?? = 4 x 3 x 2 x 48 x 47

= 81,216

Answer: 81,216 hands