Question

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

Answer 1

2 aces can be selected from 4 aces by 4C2 = 4!/2!(4 - 2)! =4!/ (2! x 2!) = (4 x 3 x 2 x 1)/(2 x 1 x 2 x 1) = 6 ways
3 kings can be selected from 4 kings by 4C3 = 4!/3!(4 - 3)! =4!/ (3! x 1!) = (4 x 3 x 2 x 1)/(3 x 2 x 1 x 1) = 4 ways

Therefore, the number of 5 card poker hands consisting of 2 aces and 3 kings possible with an ordinary 52 card deck is 6 x 4 = 24