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Question

# From a heap containing 15 pairs of shoes, 10 shoes are selected at random. The probability that there is no complete pair in the selected shoes is

A
30C10(15C10)21030C10
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B
15C10(210)30C10
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C
30C1021530C10
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D
15C1030C10
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Solution

## The correct option is B 15C10(210)30C10Out of the 15 pairs, we select any 10 in C1510 ways. Out of these 10 pairs, we need to select any one of the shoes for each pair so that a complete pair is not formed. This can be done in (C21)10=210 ways. So, favorable cases = C1510×210 ways. So, probability = C1510×210C3010

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