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Question: There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability t...

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

A

99/323

B

224/323

C

100/323

D

None

Answer

99/323

Explanation

Solution

Total number of ways = 20 x 19 x 18 x 17

The number of ways in which no pair is selected = 20 x 18 x 16 x 14

Hence the required probability = 1 - 20x18x16x1420x19x18x17=99323\frac{20x18x16x14}{20x19x18x17} = \frac{99}{323}