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प्रश्न
Three cards are drawn from a pack of 52 cards. Find the chance that they are a king, a queen, and a jack
उत्तर
3 cards can be drawn from a pack of 52 cards in 52C3 ways.
∴ n(S) = 52C3
Let event D: The cards drawn are a king, a queen, and a jack.
There are 4 kings, 4 queens, and 4 jacks in a pack of 52 cards.
∴ 1 king can be drawn from 4 kings in 4C1 ways,
1 queen can be drawn from 4 queens in 4C1 ways and
1 jack can be drawn from 4 jacks in 4C1 ways.
∴ n(D) = 4C1 × 4C1 × 4C1 = 4 × 4 × 4
∴ P(D) = `("n"("D"))/("n"("S"))`
= `(4 xx 4 xx 4)/(""^52"C"_3)`
= `(4 xx 4 xx 4)/((52 xx 51 xx 50)/(3 xx 2 xx 1)`
= `16/5525`
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