Question

The number of committees of five persons with a chair person can be selected from 12 persons, is ___________.

Answer 1

A chair person can be selected in 12 ways
Now, we need to select 4 person out of remaining 11.
∴ Number of committees of five person with a chair person can be selected in 12 × ¹¹C₄ ways
$$\begin{gathered} \mathrm{i}.\mathrm{e}12\times \frac{11!}{4!7!} \\ =\frac{12\times 11\times 10\times 9\times 8}{4\times 3\times 2} \\ =3960 \end{gathered}$$