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How many different ways can six people - ABCDEF - sit in a row at a movie theater if A and B will not sit next to each other?
Wiki User
∙ 10y ago
There are 480 ways.
The simplest way to get the answer is to find the total number of ways that they can sit and, from that, subtract the number in which A and B are next to one another.
Total number of ways = 6! = 6*5*4*3*2*1 = 720.
Now suppose A and B are next to one another. Treat AB as a single unit, and then the total number of ways is 5! = 5*4*3*2*1 = 120. But A and B can be next to one another in two ways: AB and BA. So, the total number of ways with A and B next to one another is 2*120 = 240.
That leaves 720 - 240 = 480 ways in which the six can sit in a row with A and B not together.
Wiki User
∙ 10y ago
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