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
Answer & explanation
Correct answer: option 2
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 = $\frac{^7C_3+{^7C}_5}{^9C_5}=\frac{4}{9}$