Question

6 married couples are standing in a room. if 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is-

• A. $\frac{16}{33}$
• B. $\frac{8}{33}$
• C. $\frac{17}{33}$
• D. $\frac{24}{33}$

Answer 1

Answer: (A)

$\frac{16}{33}$

Number of ways in which $4$ persons can be selected ${}^{12}{C}_4=495$

Favorable outcomes happen when the four persons are selected from three married couples. (two persons from one married couple, one person from another married couple and one person from another married couple)

Select three married couples ${(}^6{C}_3=20ways).$

Select one married couple from them ${(}^3{C}_1=3ways).$

Select two persons from that married couple $\left(1way\right).$

Select one person from second couple $\left(2ways\right).$

Select one person from third couple $\left(2ways\right).$

Therefore, the number of ways in which $4$ persons can be selected such that there is exactly one married couple among them $=20\times 3\times 2\times 2=240$

Required probability $=\frac{240}{495}=\frac{16}{33}$