Question

In how many ways can $20$ persons be seated round a table if there are $9$ chairs?

• A. $\frac{{}^{20}{P}_9}{9}$
• B. ${}^{20}{C}_9\times 8!$
• C. ${}^{20}{P}_9$
• D. none of these

Answer 1

The correct option is B ${}^{20}{C}_9\times 8!$

There are $20$ persons and $9$ chairs are available.

So select any $9$ out of $20$ and then arrange them around the round table.

${}^{20}{C}_9\times (9-1)!{=}^{20}{C}_9\times 8!$