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Two cards are drawn from a pack of 52 cards. Find the probability that one is spade and other is non-spade.

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#### Solution

Two cards can be drawn from a pack of 52 cards in ^{52}C_{2} ways.

∴ n(S) = ^{52}C_{2}

Let E be the event that out of the two cards drawn one is a spade and other is non-spade.

There are 13 spade cards and 39 cards are non-spade cards in a pack of 52 cards.

∴ One spade card can be drawn from 13 spade cards in ^{13}C_{1} ways and one non-spade card can be drawn from 39 non-spade cards in ^{39}C_{1} ways.

∴ n(E) = ^{13}C_{1} × ^{39}C_{1}

∴ P(E) = `("n"("E"))/("n"("S")`

= `(""^13"C"_1 xx ""^39"C"_1)/(""^52"C"_2)`

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