In how many ways can n women be seated in a row so that 2 particular women will not be
next to each other?
The number of ways anybody can sit anwhere is n!
The number of ways the two women sit together, is to think of those two
women as 1 pair. Then there are n-2 individuals and 1 pair, making n-1
"things" to sit in a row, so that is (n-1)!.
However the two women can sit together in two ways, the 1st woman on
the left and 2nd woman on the right or vice-versa. So we must multiply
(n-1)! by 2.
Answer: n! - 2(n-1)!
Edwin
