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प्रश्न
Four cards are drawn from a pack of 52 cards. Find the probability that all the cards are from different suit.
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उत्तर
4 cards can be drawn out of 52 cards in 52C4 ways.
∴ n(S) = 52C4
Let B be the event that all the cards drawn are of different suits.
A pack of 52 cards consists of 4 suits each containing 13 cards.
∴ A card can be drawn from each suit in 13C1 ways.
∴ 4 cards can be drawn from 4 different suits in 13C1 × 13C1 × 13C1 × 13C1 ways.
∴ n(B) = 13C1 × 13C1 × 13C1 × 13C1
∴ P(B) = `("n"("B"))/("n"("S")`
= `(""^13"C"_1 xx ""^13"C"_1 xx ""^13"C"_1 xx ""^13"C"_1)/(""^52"C"_4)`
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