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 neighbours of the president?

Question

Philoid · Accepted Answer

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

JS

P

S

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

JS

P

S

P

JS

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