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Question

There are 10 pairs of shoes in a cupboard from which 4 shoes are packed at random. The probability that there is at least one pair is


A

99323

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B

224323

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C

100323

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D

None of these

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Solution

The correct option is A

99323


Explanation of the correct option.

Step 1: Find the probability of not getting a pair.

Given: There are 10 pairs of shows, i.e. 20 shoes.

The 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 no pair is selected is 20×18×16×14.

Thus, the probability of not getting a pair is

20×18×16×1420×19×18×17=224323

Step 2: Find the probability of getting at least one pair.

Since, P(A)'=1-P(A)

Therefore, the probability of getting at least one pair is

1-224323=99323

Hence option A is the correct option.


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