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(A) Total number of cards = $52$.The total number of ways to draw $4$ cards from $52$ is $^{52}C_4 = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes

Vedclass · Accepted Answer

$\frac{72 	imes 169}{425 	imes 49}$

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(A) Total number of cards = $52$.The total number of ways to draw $4$ cards from $52$ is $^{52}C_4 = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	imes 2 	imes 1} = 270725$.For the favourable case,we need exactly two cards from one suit and one card each from two other different suits.Step $1$: Select $1$ suit out of $4$ to get $2$ cards: $^4C_1 = 4$ ways.Step $2$: Select $2$ cards from the $13$ cards of that suit: $^{13}C_2 = \frac{13 	imes 12}{2} = 78$ ways.Step $3$: Select $2$ other suits out of the remaining $3$ suits: $^3C_2 = 3$ ways.Step $4$: Select $1$ card each from these $2$ selected suits: $^{13}C_1 	imes ^{13}C_1 = 13 	imes 13 = 169$ ways.Total favourable ways = $4 	imes 78 	imes 3 	imes 169 = 157872$.Probability = $\frac{157872}{270725} = \frac{72 	imes 169}{425 	imes 49}$.

Four cards are drawn at random from a pack of playing cards. The probability of getting exactly two cards from the same suit and the remaining two cards from two different suits is

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