Question

Greg, marcia, peter, jan, bobby and cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. if marcia and jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?

Answer 1

Find the total ways that people can be seated with no restrictions;

6! ways but you know that marcia and jan will not sit together.

Write out this, as: G, (M, J), B, P <-- M and J (Marcia and Jan are grouped together to find the ways they will be sat together, so we can subtract this away).

In this combination, considering M and J as one, you have 5! ways. Then you see that M and J can switch position, so there would be added 2! ways.

In total, possibility of J and M to sit together is 5!2!

6!-5!2!
=720-240
= 480 possible ways of seating the friends so that Jan and Marcia are not together.

Hope I helped :)