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probability

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total pairs =12 total socks =24 (12 +12)

4 socks are picked  

 prob of no pair (1 x22 x 20 x 18) /(23 x 22 x 21)  = 120/161(all are one of their pair       first one may be anything 24/24   second must not be its pair(22/23) third must not be pair of first or second    20/22   fourth must not be pair of 1st 2nd or 3rd (18/21  )

probability of at least one pair=1-120/161 =41/161
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ans = one pair and other not pair  + 2 pairs

2 pairs = 12C2

One pair and other not pair = 12C1 * (10C2 - 11C1)

Thus, ans = (12C1 * (10C2 - 11C1) + 12C2) / 12C4

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