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(D) Total number of cards in a pack = $52$.Number of red cards in a pack = $26$.We need to draw $3$ cards from the $26$ red cards.The number of ways t

Vedclass · Accepted Answer

$\frac{2}{17}$

Vedclass · Answer

(D) Total number of cards in a pack = $52$.Number of red cards in a pack = $26$.We need to draw $3$ cards from the $26$ red cards.The number of ways to choose $3$ red cards out of $26$ is given by ${}^{26}C_3$.The total number of ways to choose $3$ cards out of $52$ is given by ${}^{52}C_3$.The probability $P$ is given by:$P = \frac{{}^{26}C_3}{{}^{52}C_3} = \frac{\frac{26 	imes 25 	imes 24}{3 	imes 2 	imes 1}}{\frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1}} = \frac{26 	imes 25 	imes 24}{52 	imes 51 	imes 50}$Simplifying the expression:$P = \frac{26}{52} 	imes \frac{25}{50} 	imes \frac{24}{51} = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{8}{17} = \frac{8}{68} = \frac{2}{17}$.Thus,the correct option is $D$.

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

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