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Question

# There are 10 pairs of shoes in a cupboards, from which 4 shoes are picked at random. The probability that there is at least one pair, is..........

A
101323
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B
100323
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C
99323
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D
110323
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Solution

## The correct option is B 99323The total number of ways of choosing 4 shoes (in order) out of 10 pairs (or 20 shoes) is 20×19×18×17 The number of ways in which pair is selected is 20×18×16×14Thus the probability of not getting a pair is 20×18×16×1420×19×18×17=224323Hence, the probability of getting atleast one pair is 1−224323=99323

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