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

Three 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

99323\frac { 99 } { 323 }

B

224323\frac { 224 } { 323 }

C

100323\frac { 100 } { 323 }

D

None of these

Answer

99323\frac { 99 } { 323 }

Explanation

Solution

At least one is pair = 1 – none is pairs

= 1 – 2020\frac { 20 } { 20 } × 1819\frac { 18 } { 19 } × 1618\frac { 16 } { 18 } × 1417\frac { 14 } { 17 } = 99323\frac { 99 } { 323 }