Hi All,
Since the GMAT tends to "reward" flexible thinkers, it's important to be comfortable thinking logically and in a number of different ways. I'm going to show you a way to think of this question that's more about logic and less about math.
Since there are 6 people sitting in 6 adjacent seats, using permutation logic/math makes sense.
IF there were NO restrictions, then the total number of options would be: 6x5x4x3x2x1 = 720 arrangements.
BUT there is a restriction: Marcia and Jan CAN'T sit next to one other. That means we'll have to subtract some of the options away from the 720.
Imagine if we put Marcia in seat 1 and Jan in seat 2. Then we'd have….
(M)(J)(4)(3)(2)(1) = 24 ways with Marcia 1st and Jan 2nd.
If we flipped those two around, we'd have…
(J)(M)(4)(3)(2)(1) = 24 ways with Jan 1st and Marcia 2nd.
24 + 24 = 48 ways that DON'T WORK if we put Marcia and Jan in the first 2 spots.
We can use that SAME pattern throughout the row:
2nd and 3rd = 48 options that DON'T WORK
3rd and 4th = 48 options that DON'T WORK
4th and 5th = 48 options that DON'T WORK
5th and 6th = 48 options that DON'T WORK
In total, there are 48(5) = 240 ways that DON'T WORK. Subtract those ways from the total possible.
720 - 240 = 480 arrangements.
GMAT assassins aren't born, they're made,
Rich