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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 ^{52}C_{4} ways.

∴ n(S) = ^{52}C_{4 }

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 ^{13}C_{1} ways.

∴ 4 cards can be drawn from 4 different suits in ^{13}C_{1} × ^{13}C_{1} × ^{13}C_{1} × ^{13}C_{1} ways.

∴ n(B) = ^{13}C_{1} × ^{13}C_{1} × ^{13}C_{1} × ^{13}C_{1}

∴ 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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