How Many Bridge Hands Include Specific Card Suits?

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SUMMARY

The total number of different bridge hands containing five spades, three diamonds, three clubs, and two hearts is calculated by multiplying the combinations of each suit. Specifically, the calculations are 13C5 for spades, 13C3 for diamonds, 13C3 for clubs, and 13C2 for hearts. The correct total is 8,211,173,256, achieved by multiplying these values together rather than adding them. This method resolves the initial miscalculation of 1,937.

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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?
 
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stevecallaway said:

Homework Statement

How many different bridge hands are possible containing five spaids, three diamonds, three clubs, and two hearts?
Those would be "spades."
stevecallaway said:

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.
 

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