In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

Answer: Option A

Number of ways of (selecting at least two couples among five people selected) = $$\left({}^5{C}_2\times {}^6{C}_1\right)$$
As remaining person can be any one among three couples left.
Required probability
$$\begin{array}{rl}& =\frac{{}^5{C}_2\times {}^6{C}_1}{{}^{10}{C}_5}\\ & =\frac{\left(10\times 6\right)}{252}\\ & =\frac{5}{21}\end{array}$$