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Question

(C) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$.${}^{52}C_3 = \frac{52 	imes 51 	imes 50}{3 	imes

Vedclass · Accepted Answer

$\frac{1}{5525}$

Vedclass · Answer

(C) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$.${}^{52}C_3 = \frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1} = 52 	imes 17 	imes 25 = 22100$.There are $4$ aces in a pack of $52$ cards. The number of ways to draw $3$ aces from $4$ is given by ${}^{4}C_3$.${}^{4}C_3 = \frac{4 	imes 3 	imes 2}{3 	imes 2 	imes 1} = 4$.The probability of drawing $3$ aces is $\frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{{}^{4}C_3}{{}^{52}C_3} = \frac{4}{22100} = \frac{1}{5525}$.

Three cards are drawn at random from a pack of $52$ cards. What is the chance of drawing three aces?

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