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Imagine arranging 6 people to sit on a bench and 3 of them have to sit side by side. How many relevant arrangements will be made?

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Question:

A
144

explanation

Consider the relative positions of the 3 people. Let's say the 3 people who have to sit together are A, B, and C. We can think of the different arrangements as follows:

A B C (all 3 are together)

A C B

B A C

B C A

C A B

C B A

There are 6 ways to arrange the 3 people within their unit. But for each of these arrangements, the 3 people can also be switched around within their unit, so the total number of ways is 6 × 3! = 144.

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