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Question

(A) Total number of ways to draw $4$ cards from $52$ cards is $^{52}C_4$. To get exactly two cards from the same suit and the remaining two cards from

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Total number of ways to draw $4$ cards from $52$ cards is $^{52}C_4$. To get exactly two cards from the same suit and the remaining two cards from two different suits: $1$. Select $1$ suit out of $4$ for the pair: $^4C_1$. $2$. Select $2$ cards from the $13$ cards of that suit: $^{13}C_2$. $3$. Select $2$ suits out of the remaining $3$ for the other two cards: $^3C_2$. $4$. Select $1$ card from each of these $2$ chosen suits: $^{13}C_1 	imes ^{13}C_1$. Required probability = $\frac{^4C_1 	imes ^{13}C_2 	imes ^3C_2 	imes ^{13}C_1 	imes ^{13}C_1}{^{52}C_4}$ $= \frac{4 	imes 78 	imes 3 	imes 13 	imes 13}{270725} = \frac{12 	imes 78 	imes 169}{270725} = \frac{158184}{270725} = \frac{72 	imes 169}{425 	imes 49}$.

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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