Question

In how many ways can 7 people be lined up in a row for a picture if two of them should have at least 2 people between them?

Answer 1

A hint would be to first
Consider drawing 7 slots for the people then organizing how many ways the line up can go...
Doris, _____, ______ Paul,_______, _______, ________ but then
_____, Doris, _______, _______, Paul,_____, ______ and then
_____, _____, Doris, ______, _______, Paul, _______ and then
_____, _____, _____, Doris, ______, _______, Paul but you could have Paul first and Doris second so you have to times by 2 for that arrangement.
So there are 4 ways Doris and Paul can be placed, then times by 2 for the Paul then Doris scenerio,
that is 4 x 2 x now the other 5 people are placed in the spots (so 5!)
4 x 2 x 5 x 4 x 3 x 2 x 1
now consider the word "at least" in the question...