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(C) The total number of ways to draw $2$ cards from $52$ cards is given by $^{52}C_2$. The number of ways to draw $2$ cards of spade from $13$ spade c

Vedclass · Accepted Answer

$\frac{1}{17}$

Vedclass · Answer

(C) The total number of ways to draw $2$ cards from $52$ cards is given by $^{52}C_2$. The number of ways to draw $2$ cards of spade from $13$ spade cards is given by $^{13}C_2$. The required probability is $P = \frac{^{13}C_2}{^{52}C_2}$. $P = \frac{\frac{13 	imes 12}{2 	imes 1}}{\frac{52 	imes 51}{2 	imes 1}} = \frac{13 	imes 12}{52 	imes 51} = \frac{1 	imes 12}{4 	imes 51} = \frac{12}{204} = \frac{1}{17}$. Thus,the correct option is $C$.

Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of spade is

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