From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ? Correct Answer 7250100

There are 13 spades,we must include 2: 13C2

 

There are 13 diamonds,we must include 3: 13C3

 

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : 26C2

 

Therefore,13C2*13C3*26C2 = 7250100

Bissoy MCQ

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