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Question

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?


Solution

From a pack of 52 cards, 4 cards can be drawn in 52C4 ways.
There are 13 cards of diamond and 13 cards of spades
Now 3 cards of diamond out of 13 cards of diamond can be drawn in 13C3 ways and 1 card of spade out of 13 cards of spade can be drawn in 13C1 ways.
Thus the probability of obtaining 3 diamond and 1 spade card
=13C3×13C152C4
 

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