In how many ways can 6 students sit in a row, if two of the students do not want to sit next to each other?
Let us suppose that they DO want to sit next to each other
They can be seated in any of 5 poistions, each can be arranged in two ways and for each of these the other 4 students can be arranged in 4! =24 ways
So......we have 5 * 2 * 24 = 240 ways
And the ways they can be arranged where the two students do not want to sit next to each other =
total arrangements - 240 =
6! - 240 =
720 - 240 =