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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

100223\frac { 100 } { 223 }

B

99323\frac { 99 } { 323 }

C

224323\frac { 224 } { 323 }

D

None of these

Answer

99323\frac { 99 } { 323 }

Explanation

Solution

Total ways = 20C4 =

= 20×19×18×174×3×2\frac { 20 \times 19 \times 18 \times 17 } { 4 \times 3 \times 2 } = 15 × 19 × 17 = 4845

No. of ways in which no pair occurs

= 20×18×16×1444\frac { 20 \times 18 \times 16 \times 14 } { 44 } = 3360

Prob. alteast one pair occur = 4845−33604845\frac { 4845 - 3360 } { 4845 }

= 14854845\frac { 1485 } { 4845 } = 297969\frac { 297 } { 969 } = 99323\frac { 99 } { 323 }