# How many 5-card hands make full house

• June 4th 2009, 11:01 AM
Twig
How many 5-card hands make full house
Hi

I have the feeling I am wrong somewhere, I try to calculate the number of 5-card hands that make full house.

$13\cdot \binom{4}{3}\cdot 12 \cdot \binom{4}{2}$

thanks
• June 4th 2009, 12:58 PM
Soroban
Hello, Twig!

Quote:

I try to calculate the number of 5-card hands that make Full House.

. . $13\cdot \binom{4}{3}\cdot 12 \cdot \binom{4}{2}$

. . $\begin{array}{cc}\text{Number of values for the Triple:} & 13 \\
\text{Number of ways to get the Triple:} & {4\choose3} \\
\text{Number of values for the Pair:} & 12 \\
\text{Number of ways to get the Pair:} & {4\choose2} \end{array}$

Absolutely correct!