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

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(A) Total number of ways to draw a hand of $7$ cards from $52$ cards is given by $^{52}C_{7}$.To have all $4$ Kings in the hand,we must select all $4$

Vedclass · Accepted Answer

$\frac{1}{7735}$

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(A) Total number of ways to draw a hand of $7$ cards from $52$ cards is given by $^{52}C_{7}$.To have all $4$ Kings in the hand,we must select all $4$ Kings from the $4$ available Kings and the remaining $7 - 4 = 3$ cards from the remaining $52 - 4 = 48$ cards.Number of favorable outcomes $= ^{4}C_{4} 	imes ^{48}C_{3}$.Probability $P = \frac{^{4}C_{4} 	imes ^{48}C_{3}}{^{52}C_{7}}$.Calculating the values:$^{4}C_{4} = 1$.$^{48}C_{3} = \frac{48 	imes 47 	imes 46}{3 	imes 2 	imes 1} = 17296$.$^{52}C_{7} = \frac{52 	imes 51 	imes 50 	imes 49 	imes 48 	imes 47 	imes 46}{7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 133784560$.$P = \frac{17296}{133784560} = \frac{1}{7735}$.

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains all $4$ Kings.

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