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14.Probability
hard
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
