Question

A round table conference is to be held among 20 countries. If two particular delegates wish to sit together, then such arrangements can be done in __________ways.

• A. 18!
• B. \(\frac {19!}{2!}\)
• C. 2 * 18!
• D. 19! * 2!

Answer 1

The Correct Option is C

If two particular delegates wish to sit together in a round table conference among 20 countries, we can consider these two delegates as a single entity or pair. So, we have 19 entities (18 countries + 1 pair of delegates) to arrange around the table. 
The number of ways to arrange these entities in a circular arrangement is (n-1)!, where n is the number of entities. 
Therefore, the number of ways to arrange 19 entities in a circular arrangement is (19-1)! = 18! However, since the two particular delegates in the pair can be arranged among themselves in 2! = 2 ways, we need to multiply the above result by 2 to account for the arrangements within the pair. 
Hence, the total number of ways to arrange the entities when the two particular delegates sit together in a round table conference among 20 countries is: 18! * 2
Theredfore, the correct option is (C) 2 * 18!