Question

The are 5 pairs of shoes in a shoe rack. Four shoes are drawn one by one at random. Find the probability that at least one pair of shoes is drawn.

Answer 1

Let P = no pair of shoes were chosen

$\Rightarrow$ we have to select four power to take 1 shoes from each of them out of 5 = ${}^5{C}_4$ and 2 choice for each${=}^5{C}_4\times 2$

& Total choice = ${}^{10}{C}_4\Rightarrow P=\frac{2{\times }^5{C}_4}{{}^{10}{C}_4}=\frac{10}{{}^{10}{C}_4}$

Required probability = 1- P = 1 - $\frac{10}{{}^{10}{C}_4}=1-10\times 24$

$=1-\frac{1}{21}=\frac{20}{21}$