if five cards are drawn from an orfinary dech 52 cards, How many ways are there of getting all hearts?

Question

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Answer 1

Recall that the number of ways to choose k objects from a set of n objects is the binomial coefficient

 

C(n,k) = n! / [k! (n-k)!]

 

There are n = 13 hearts in the deck and you are choosing k = 5 cards so the number of hands are

 

C(13,5) = 13! / (5! 8!) = 13·12·11·10·9 / 120 = 13·11·9 = 1287