Maharashtra State BoardHSC Commerce 11th
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Four cards are drawn from a pack of 52 cards. Find the probability that all the cards are from different suit. - Mathematics and Statistics

Sum

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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Solution

4 cards can be drawn out of 52 cards in 52C4 ways.
∴ n(S) = 52C
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)`

Concept: Elementary Properties of Probability
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