4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
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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Number of ways of drawing 4 cards from 52 cards = 52C4
In a deck of 52 cards, there are 13 diamonds and 13 spades.
∴ Number of ways of drawing 3 diamonds and one spade = 13C3 x 13C1
Thus, the probability of obtaining 3 diamonds and one spade =13C3 x 13C1 / 52C4
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4 cards can be drawn from 52 in 52C4 ways.
P(3 diamond and one spade)
= (C3 x 13C1)/52C4 = 286/20825
∵ 13 diamond cards and 13 spade cards in a pack of [1] cards.
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