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(D) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$. There are $26$ red cards in a pack of $52$. The num

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$\frac{2}{17}$

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(D) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$. There are $26$ red cards in a pack of $52$. The number of ways to draw $3$ red cards is ${}^{26}C_3$. $	ext{Required probability} = \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: $\frac{26}{52} 	imes \frac{25}{50} 	imes \frac{24}{51} = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{8}{17} = \frac{8}{68} = \frac{2}{17}$.

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

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