In how many ways can a full house of three jacks and two tens be obtained?
A) 10
B) 24
C) 28
D) 32
E) 6

Question

In how many ways can a full house of three jacks and two tens be obtained? ​
A) 10
B) 24
C) 28
D) 32
E) 6

Quizplus · Accepted Answer

A full house in poker consists of three cards of one rank and two cards of another. For three jacks, there are $ \binom{4}{3} = 4 $ ways to choose which three of the four jacks to include. For two tens, there are $ \binom{4}{2} = 6 $ ways to choose which two of the four tens to include. Multiplying these together gives $ 4 \times 6 = 24 $ ways to get a full house of three jacks and two tens.

In How Many Ways Can a Full House of Three