Question

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

Answer 1

This is a question on combination.

A combination of n objects picked k at a time.

The combination formula is :

ⁿCk = $\frac{n! }{k! (n - k)! }$

In our case :

n = 20

k = 9

Doing the substitution we have :

²⁰C₉ = $\frac{20!}{9!(20 - 9)!}$

= $\frac{20!}{9!11!}$

= 167960 ways