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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?
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Solution
Number of ways to drawn 4 cards from a deck of 52 cards = 52C4
∴ n(S) = 52C4
Number of ways to obtain 3 diamonds = 13C3
Number of ways to drawn 1 spade = 13C1
Number of ways to drawn 3 diamonds and one spade = 13C3 × 13C1
Total number of favourable outcomes = 13C3 × 13C1
Hence, the probability of obtaining 3 diamonds and 1 spade = `(""^13C_3 xx ""^13C_1)/(""^52C_4)`
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