Question

Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are always together.

Answer 1

Delegates of 24 countries are to participate in a round table discussion such that two specified delegates are always together.
Let us consider these 2 delegates as one unit.
They can be arranged among themselves in 2! ways.
Also, these two delegates are to be seated with 22 other delegates (i.e. total 23) which can be done in (23 − 1)! = 22! ways
∴ Total number of arrangement if two specified delegates are always together
= 22! × 2!