Maharashtra State BoardHSC Science (General) 11th
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Three cards are drawn from a pack of 52 cards. Find the chance that they are a king, a queen and a jack - Mathematics and Statistics

Sum

Three cards are drawn from a pack of 52 cards. Find the chance that they are a king, a queen, and a jack

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Solution

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`

Concept: Concept of Probability
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