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Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and

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Re: Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and [#permalink]

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New post 26 Mar 2018, 14:01
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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.

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Rich
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Re: Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and   [#permalink] 26 Mar 2018, 14:01
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