A committee of the five is to be chosen from a group of people. The probability that a certain married couple will either serve together or not at all is |
$\frac{2}{3}$ $\frac{4}{9}$ $\frac{1}{2}$ $\frac{5}{9}$ |
$\frac{4}{9}$ |
From a group of 9 people, 5 people can be chosen in ${^9C}_5$ ways. ∴ Total number of ways of forming the committee = ${^9C}_5$ The number of ways in which a certain married couple is either in the committee or it is not included in the committee, is ${^7C}_3 × {^2C}_2 + {^7C}_5$ Hence, required probability = $\frac{^7C_3+{^7C}_5}{^9C_5}=\frac{4}{9}$ |