A committee consists of 20 persons in how many ways can the members sit around a circular table so that the chairman sits between the secretary and the treasurer?

Question

A committee consists of 20 persons,in how many ways can the members sist around a circular table so that the chairman sits between the secretary and the treasurer?

Answer 1

There are two ways for the secretary (S) to sit between the chairman (C) and treasurer (T): CST and TSC. The remaining 17 committee members can arrange themselves 17! ways (3.557*10^14 approx), because, if we place one member out of the 17 in a particular position, there are 16 places left for the next member, then 15, and so on. So the total number is 17*16*15*...*1=17! (17 factorial). We need to double this for all 20 persons because there are two ways for C, S and T. Then, we need to allow for the round table, so that's another factor of 20. In all then, we have 40*17!=1.4227*10^16 approx.