Find the probability that when a hand of 7 ca | vedclass

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Question

(A) The total number of ways to draw $7$ cards from $52$ cards is given by $^{52}C_{7}$.To have exactly $3$ Kings,we must choose $3$ Kings from the $4

Vedclass · Accepted Answer

$\frac{9}{1547}$

Vedclass · Answer

(A) The total number of ways to draw $7$ cards from $52$ cards is given by $^{52}C_{7}$.To have exactly $3$ Kings,we must choose $3$ Kings from the $4$ available Kings and $4$ non-King cards from the remaining $48$ cards.The number of ways to choose $3$ Kings is $^{4}C_{3} = 4$.The number of ways to choose $4$ non-King cards is $^{48}C_{4} = \frac{48 	imes 47 	imes 46 	imes 45}{4 	imes 3 	imes 2 	imes 1} = 194580$.The total number of favorable outcomes is $^{4}C_{3} 	imes ^{48}C_{4} = 4 	imes 194580 = 778320$.The total number of possible outcomes is $^{52}C_{7} = 133784560$.The probability $P$ is $\frac{778320}{133784560} = \frac{9}{1547}$.

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains exactly $3$ Kings.

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