There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. probability that

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14.Probability

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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

$\frac{{99}}{{323}}$

B

$\frac{{224}}{{323}}$

C

$\frac{{100}}{{323}}$

D

None of these

Solution

(a) Total number of ways $ = 20 \times 19 \times 18 \times 17$

The number of ways in which no pair is selected $ = 20 \times 18 \times 16 \times 14$

Hence the required probability

$ = 1 – \frac{{20 \times 18 \times 16 \times 14}}{{20 \times 19 \times 18 \times 17}} = \frac{{99}}{{323}}.$

Standard 11

Mathematics

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