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Question
Four cards are drawn from a pack of 52 cards. Find the probability that 3 are king and 1 is jack.
Solution
4 cards can be drawn out of 52 cards in 52C4 ways.
∴ n(S) = 52C4
Let A be the event that out of the four cards drawn, 3 are kings and 1 is a jack.
There are 4 kings and 4 jacks in a pack of 52 cards.
∴ 3 kings can be drawn from 4 kings in 4C3 ways.
Similarly, 1 jack can be drawn out of 4 jacks in 4C1 ways.
∴ Total number of ways in which 3 kings and 1 jack can be drawn is 4C3 × 4C1.
∴ n(A) = 4C3 × 4C1
∴ P(A) = `("n"("A"))/("n"("S")`
= `(""^4"C"_3 xx ""^4"C"_1)/(""^52"C"_4)`
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