1
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Question

# There are 10 pairs of shoes in a cup board from which 4 shoes are picked 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
25
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D
35
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Solution

## The correct option is B 9932310 pairs=20shoesProbability of atleast 1 pair=1−Probability of no pairFirst shoe has 20 choicesSecond shoe has 18 choicesThird shoe has 16 choicesFourth shoe has 14 choicesProbability of atleast 1 pair=1−Probability of no pair.=1−2020.1819.1618.1417=1−16×1419×17=1−224323=99323

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