Question 770591
In how many ways can n women be seated in a row so that 2 particular women will not be
next to each other?
<pre>
{{{Answer}}}{{{""=""}}}{{{(matrix(8,1,

The, number, of, ways, anybody, can, sit, anywhere))}}}{{{""-""}}}{{{(matrix(9,1,

The, number, of, ways, those, two, women, sit,together))}}}

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</pre>