From a pack of 52 playing cards,three cards a | vedclass

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Question

(B) The total number of ways to select $3$ cards from $52$ cards is given by ${}^{52}C_{3} = \frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1} = 2210

Vedclass · Accepted Answer

$\frac{16}{5525}$

Vedclass · Answer

(B) The total number of ways to select $3$ cards from $52$ cards is given by ${}^{52}C_{3} = \frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1} = 22100$.Let $E$ be the event of drawing one king,one queen,and one jack.The number of ways to select $1$ king from $4$ kings,$1$ queen from $4$ queens,and $1$ jack from $4$ jacks is:$n(E) = {}^{4}C_{1} 	imes {}^{4}C_{1} 	imes {}^{4}C_{1} = 4 	imes 4 	imes 4 = 64$.The probability $P(E)$ is given by:$P(E) = \frac{n(E)}{n(S)} = \frac{64}{22100}$.Simplifying the fraction by dividing both numerator and denominator by $4$:$P(E) = \frac{16}{5525}$.

From a pack of $52$ playing cards,three cards are drawn at random. Find the probability of drawing a king,a queen,and a jack.

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