The probability that the three cards drawn fr | vedclass

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Question

(D) Total number of ways to draw $3$ cards from $52$ cards is $^{52}C_{3}$.Number of red cards in a pack is $26$.Number of ways to draw $3$ red cards

Vedclass · Accepted Answer

$\frac{2}{17}$

Vedclass · Answer

(D) Total number of ways to draw $3$ cards from $52$ cards is $^{52}C_{3}$.Number of red cards in a pack is $26$.Number of ways to draw $3$ red cards from $26$ red cards is $^{26}C_{3}$.The probability $P$ is given by:$P = \frac{^{26}C_{3}}{^{52}C_{3}} = \frac{\frac{26 	imes 25 	imes 24}{3 	imes 2 	imes 1}}{\frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1}} = \frac{26 	imes 25 	imes 24}{52 	imes 51 	imes 50}$$P = \frac{26}{52} 	imes \frac{25}{50} 	imes \frac{24}{51} = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{8}{17} = \frac{8}{68} = \frac{2}{17}$.

The probability that the three cards drawn from a pack of $52$ cards are all red is

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