Question

In how many ways can 11 members of a committee sit at a round table so that the secretary and the joint secretary are always the neighbour of the president?

Answer 1

First assume the president(P), Joint secretary(JS) and secretary(S) to be 1 members(as shown below)

So there are 9 members, a number of ways to arrange this 9 people is 8! (The formula used (n-1)!) 

Now we need to look at the internal arrangement. There are 2 arrangement possible

So total number of arrangement are (8!) × 2 = 80,640