SOLUTION: How many 5-card hands out of a 52-card deck are full house? Full house is formed by any three cards of the same denominations plus any pair of a different denomination.

Algebra ->  Permutations -> SOLUTION: How many 5-card hands out of a 52-card deck are full house? Full house is formed by any three cards of the same denominations plus any pair of a different denomination.      Log On


   

Question 1096397: How many 5-card hands out of a 52-card deck are full house? Full house is
formed by any three cards of the same denominations plus any pair of a different denomination.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Choose the denomination for the three cards with the same denomination
in any of 13 ways.
Choose a different denomination for the pair in any of the remaining
12 ways.
Choose the suits for the three cards any of "4 suits choose 3" or 4C3 
ways.
Choose the suits for the pair any of "4 suits choose 2" or 4C2 
ways.

Answer: 13×12×(4C3)×(4C2) = 13×12×4×6 = 3744 ways to have a full house.

Edwin