A bag contains 12 pairs of socks. If 4 socks | vedclass

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(D) Total number of socks = $12 	imes 2 = 24$.Total ways to pick $4$ socks from $24$ is $^{24}C_4 = \frac{24 	imes 23 	imes 22 	imes 21}{4 	imes

Vedclass · Accepted Answer

$\frac{41}{161}$

Vedclass · Answer

(D) Total number of socks = $12 	imes 2 = 24$.Total ways to pick $4$ socks from $24$ is $^{24}C_4 = \frac{24 	imes 23 	imes 22 	imes 21}{4 	imes 3 	imes 2 	imes 1} = 10626$.To find the probability of getting at least one pair,we first find the probability of getting no pairs.To get no pairs,we must pick $4$ socks from $12$ different pairs such that no two socks form a pair. This means we choose $4$ pairs out of $12$ and then choose $1$ sock from each of those $4$ pairs.Number of ways to get no pairs = $^{12}C_4 	imes 2^4 = 495 	imes 16 = 7920$.Probability of getting no pair = $\frac{7920}{10626} = \frac{120}{161}$.Therefore,the probability of getting at least one pair = $1 - \frac{120}{161} = \frac{41}{161}$.

$A$ bag contains $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to

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