Question

There are 5 pairs of shoes in a shoe rack. Four shoes are drawn one by one at random. The probability that at least one pair of shoes is drawn is $1-\frac{k}{21}$. Find the value of $k$.

Answer 1

The probability that at least one pair is drawn
$=1-$(None of them is a pair)
$=1-\frac{10}{10}.\frac{8}{9}\cdot \frac{6}{8}\cdot \frac{4}{7}=1-\frac{8}{21}=\frac{13}{21}$