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in how many ways can 6 students be seated in a round table of 6 seats if 2 of the students insist on sitting beside each other? ​

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We can treat this as 5 items arranged in a row. There are 5! ways to arrange them: 5*4*3*2*1=120 ways. For each of those ways, the “item” that is the two students who insist on sitting together, can be arranged in two ways. So, 240 total ways.

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