Latest Elitmus Aptitude Question SOLUTION: There are ten pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is

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(#M40040024) ELITMUS Category question Keep an EYE

There are ten pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is

Asked In Elitmus Dada Khalandar (9 years ago)

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khushboo goenka  (9 years ago)

105/323
total chhances=20c4
10c1*18c2+10c2/20c4

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Komal Kumbhare  (9 years ago)

Case 1 A pair in 2nd draw = 1*1/19
Case 2 A pair in 3rd draw = 1*18/19*2/18
case 3 A pair in 4th draw = 1*18/19*16/18*3/17

Ans = sum of all 3 = 99/323

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Akash kumar  (9 years ago)

The way we can select no pair of socks is:
Select one sock from 20 sock in the first pick. In the second draw exclude the pair of the first selected sock and pick from the remaining 18 socks and so on.
= 20C1 * 18C1 * 16C1 * 14C1/4!
So required probability: 1 - ((20C1 * 18C1 * 16C1 * 14C1/4!)/20C4) = 99/323

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