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Question

A closet contains 10 pairs of shoes, If 8 shoes are selected randomly, what is the probability that there will be exactly 1 complete pair

A
17924199
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B
17824199
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C
17724199
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D
17624199
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Solution

The correct option is A 17924199
Total way to choose 8 shoes from 20 shoes =20C8
Way to choose one complete pair in 10 pair =10C1
Way to choose one complete pair in 10 pair on selecting 8 shoes is selecting 6 pairs in remaining 9 and selecting any one by 2 ways=9C6×26×10
probability=9C6×26×10/20C8=1792/4199














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