How Many Bridge Hands Include Specific Card Suits?

[stevecallaway]

Homework Statement

How many different bridge hands are possible containing five spaids, three diamonds, three clubs, and two hearts?

Homework Equations

The Attempt at a Solution

Total number of hands in which I can get 5 spaids is 13C5
Total number of hands in which I can get 3 diamonds is 13C3
Total number of hands in which I can get 3 clubs is 13C3
Total number of hands in which I can get 2 hearts is 13C2
Adding these up gives 1937 which is not any where close to 8,211,173,256.
Help?

 

[Mark44]

Homework Statement

How many different bridge hands are possible containing five spaids, three diamonds, three clubs, and two hearts?

Those would be "spades."

Homework Equations

The Attempt at a Solution

Total number of hands in which I can get 5 spaids is 13C5
Total number of hands in which I can get 3 diamonds is 13C3
Total number of hands in which I can get 3 clubs is 13C3
Total number of hands in which I can get 2 hearts is 13C2
Adding these up gives 1937 which is not any where close to 8,211,173,256.
Help?

Multiply all four numbers together and you get the right result.