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?

A. $$\frac{{5}}{{21}}$$

B. $$\frac{{5}}{{14}}$$

C. $$\frac{{9}}{{14}}$$

D. $$\frac{{16}}{{21}}$$

Answer: Option A

Solution(By Examveda Team)

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
$$\eqalign{ & = \frac{{{}^5{C_2} \times {}^6{C_1}}}{{{}^{10}{C_5}}} \cr & = \frac{{\left( {10 \times 6} \right)}}{{252}} \cr & = \frac{5}{{21}} \cr} $$