Question

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

• A. $6720$
• B. $56$
• C. $30$
• D. $346$

Answer 1

The correct option is B $56$

there are 9 chairs and 6 persons.

out of which one is guest and has a special chair.

$\Rightarrow$ 8 chairs are left for 5 persons.

so, no of ways $=8_{C_5}$

$\frac{8!}{5!\times 3!}=\frac{8\times 7\times 6\times 5!}{5!\times 3!}$

$\Rightarrow$56 ways.