A committee of five is to be chosen from a group of 9 persons. The number of ways in which this can

Question

A committee of five is to be chosen from a group of 9 persons. The number of ways in which this can be done if two persons will either serve together or not at all is

Professor PC Thomas Classes · Answer

Let A and B be the two particular persons. Number of committies including A and B is ${ }^7 \mathrm{C}_3$. Number of committies including neither A nor B is ${ }^7 \mathrm{C}_5$. Total ${ }^7 \mathrm{C}_3+{ }^7 \mathrm{C}_5$