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(C) Total number of ways to draw $2$ cards from $52$ cards is given by $^{52}C_2$.Number of ways to draw $2$ spade cards from $13$ spade cards is give

Vedclass · Accepted Answer

$\frac{1}{17}$

Vedclass · Answer

(C) Total number of ways to draw $2$ cards from $52$ cards is given by $^{52}C_2$.Number of ways to draw $2$ spade cards from $13$ spade cards is given by $^{13}C_2$.The required probability is $P = \frac{^{13}C_2}{^{52}C_2}$.Calculating the combinations: $^{13}C_2 = \frac{13 	imes 12}{2 	imes 1} = 78$ and $^{52}C_2 = \frac{52 	imes 51}{2 	imes 1} = 1326$.Thus,$P = \frac{78}{1326} = \frac{1}{17}$.

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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