Math Help - DATA

[RyanHB]

This is the question -

A bridge Hand consists of 13 cards. How many bridge hands include 5 cards of one suit, 6 cards of a second, and 2 cards of a third. Deck has 52 cards btw.

It's so simple, but after transitioning to university, I lost all data knowledge..ANy help? BTW the answer is 4 billion something.. The books gives us the answer, but I forget how to do this..

[TheGuardian001]

I believe (I never was great at this, even when I knew it, so I may be way off) that the you need to do something like this

((13 choose 6)*4) * ((13 choose 5)*3) * ((13 choose 2)*2)


13 choose N will get you the number of combinations of N cards in one suit.
Multiplying that by the number of suits available (4 for the first, 3 for the second, since we exclude the one chosen by the first, and so on) gets you the total combinations per N cards.
Multiplying all of those numbers together will get you the total number of combinations of all sets across all suits.

I got 4 134 297 024 combinations, which seems like the right number.