Solving a Distribution Problem with 52 Cards: 3 piles of 8, 4 piles of 7

[beanryu]

Homework Statement

How many ways can a deck of 52 cards be broken up into a collection of unordered piles of sizes:

Three piles of 8 cards and four piles of 7 cards?

Homework Equations

The Attempt at a Solution

ohkay, the first step i used is to think of the different piles as labels and find all possible distribution of these labels among the 52 cards, that is equal to
(51!)/((7!)^4*(8!)^3)
but i don't know what to do next.

Thankyou for your help!

 

[matt grime]

Try doing some smaller problems with fewer cards and fewer piles to see what you need to do.