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?
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 $(8 !) \times 2=80,640$