Hi, I just can't seem to figure this question out so here it is, any help would be greatly appreciated.

Using a standard deck of cards, how many bridge hands (13 cards) contain 5 spades, 2 hearts, 3 diamonds and 3 clubs?

Printable View

- Sep 24th 2008, 03:32 PMgordomacCombinations & Permutations Help
Hi, I just can't seem to figure this question out so here it is, any help would be greatly appreciated.

Using a standard deck of cards, how many bridge hands (13 cards) contain 5 spades, 2 hearts, 3 diamonds and 3 clubs? - Sep 24th 2008, 03:48 PMSoroban
Hello, gordomac!

Quote:

Using a standard deck of cards, how many bridge hands (13 cards)

contain 5 spades, 2 hearts, 3 diamonds and 3 clubs?

$\displaystyle {13\choose5}{13\choose2}{13\choose3}{13\choose3} \;=\;\frac{13!}{5!\,8!}\cdot\frac{13!}{2!\,11!}\cd ot\frac{13}{3!\,10!}\cdot\frac{13!}{3!\,10!}$

. . $\displaystyle = \;1287\cdot 78 \cdot 286 \cdot 286 \;=\;8,211,173,256 $