There are 7 pairs of shoes in a cupboard from which 6 shoes are picked at random The probability of ...........

Quantitative Aptitude (CDS) Probability

There are 7 pairs of shoes in a cupboard from which 6 shoes are picked at random. The probability of getting at least one pair is?

1/64

1/365

365/429

1/429

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Explanation:

There are 7 pair of shoes and 6 shoes can be picked in
14×13×12×11×10×9 ways.
Number of ways in which 6 shoes can be picked such that no two are alike
14×12×10×8×6×4 ways.
Therefore, the required probability = 1 – (14×12×10×8×6×4)/14×13×12×11×10×9
= 1 – 64/429
= 365/429