Question 647599
"if A and B must sit by each other", then A and B can be thought of as the same person. Think of this person as AB.


So 

A,B,C,D,E,F and G

becomes

AB,C,D,E,F and G


So you now have 7-1 = 6 people filling 6 seats. So there are 6! = 720 different ways to fill these seats.


This is also true for BA. So we double the count to 1440


Therefore, there are 1440 different ways to seat 7 people where A and B must sit by each other.