Question

Four cards are drawn from a pack of 52 cards. Find the probability that 3 are king and 1 is jack.

Answer 1

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)`