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Question

20 pairs of shoes are there in a closet. Four shoes are selected at random. The probability that there is at least one pair is

A
4040×3839×3638×3437
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B
14040×3839×3638×3437
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C
120C440C4
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D
140C420C4
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Solution

The correct option is B 14040×3839×3638×3437
Since we have 20 pairs of shoes i.e. 40 shoes and we need the probability such that there is atleast one pair of shoes, we subtract the probability of getting no pair of shoes from 1.
Probability of getting no pair = 4040×3839×3638×3437
The explanation for the above expression is that initially we are free to choose any shoe out of 40, after that we cannot choose the other paired shoe remaining in the box of the one we have already chosen and so we are left with 38 possibilities.
Proceed similarly to get the answer.
The answer to the question asked thus becomes 14040×3839×3638×3437

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