SOLUTION: how many ways can 7 people A,B,C,D,E,F and G, sit in a row at a movie theater if A and B must sit by each other?

Algebra ->  Permutations -> SOLUTION: how many ways can 7 people A,B,C,D,E,F and G, sit in a row at a movie theater if A and B must sit by each other?      Log On


   

Question 647599: how many ways can 7 people A,B,C,D,E,F and G, sit in a row at a movie theater if A and B must sit by each other?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"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.