Maharashtra State BoardHSC Arts 11th
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Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit - Mathematics and Statistics

Sum

Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit

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Solution

3 cards can be drawn from a pack of 52 cards in 52C3 ways.

∴ n(S) = 52C3

Let event C: All the cards drawn are from the same suit.

A pack of 52 cards consists of 4 suits each containing 13 cards.

∴ 3 cards can be drawn from the same suit in 13C3

∴ n(C) = 13C3 × 4

∴ P(C) = `("n"("C"))/("n"("S"))`

= `(4 xx ""^13"C"_3)/(""^52"C"_3)`

= `(4 xx 13 xx 12 xx 11)/(52 xx 51 xx 50)`

= `22/425`

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