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

Question

Mathematics

Ibarra

1 January, 22:16

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

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Julianna Simpson · 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