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(D) The total number of ways to draw $2$ cards from a pack of $52$ cards is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total

Vedclass · Accepted Answer

$\frac{1}{221}$

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(D) The total number of ways to draw $2$ cards from a pack of $52$ cards is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total outcomes $= {}^{52}C_{2} = \frac{52 	imes 51}{2 	imes 1} = 26 	imes 51 = 1326$.There are $4$ kings in a standard pack of $52$ cards. The number of ways to draw $2$ kings from $4$ is:Favorable outcomes $= {}^{4}C_{2} = \frac{4 	imes 3}{2 	imes 1} = 6$.The probability $P(E)$ of drawing $2$ kings is the ratio of favorable outcomes to total outcomes:$P(E) = \frac{6}{1326} = \frac{1}{221}$.

From a pack of $52$ cards,two cards are drawn together at random. What is the probability of both cards being kings?

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