Question

There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit?

• A. $6720$
• B. $60480$
• C. $30$
• D. $346$

Answer 1

The correct option is A

$6720$

Explanation of the correct option

Given, there are $9$ chairs and $6$ persons to be seated and One chair is specific for the guest.

Thus, we have $8$ chairs and $5$ persons to be seated and these $5$ person can change their position among them.

Therefore, total number of ways is

$\begin{array}{rcl}& =& {}^8\mathrm{C}_5\times 5!\\ & =& \frac{8!}{5!\times 3!}\times 5!\\ & =& \frac{8\times 7\times 6\times 5\times 4\times 3!}{3!}\\ & =& 6720\end{array}$

Hence option $\left(\mathrm{A}\right)$, $6720$ is the correct option.