Q3 of 140 Page 317

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?

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










S



P



JS



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


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