At a round table with five seats, how many different arrangements can a group of five friends, including Alex and Jamie, sit if Alex and Jamie cannot sit next to each other?

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Official Explanation

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To find the number of seating arrangements where Alex and Jamie do not sit together, we first calculate the total arrangements without restrictions. For a round table with five people, the number of arrangements is given by (5-1)! = 4! = 24. Next, we calculate the arrangements where Alex and Jamie are sitting together. We can treat Alex and Jamie as a single unit, which gives us four units to arrange (the…

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Comments

raspberrynutApr 28, 2025

thanksss

ArvindMar 17, 2024

Thankss

YuJun 28, 2024

appreciated!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.