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six people are seated around acircular table while dining in a restaurant in how many ways can they be arranged?​

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GoroMizusaike23viz

Answer:

6 People in a round table can be seated in (6 - 1) ! ways = 120.

Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5.

We can consider as if 5 people are sitting in a row because it is round table.

Again consider 3 people, those who can not sit together, as a single unit –

So the possible arrangements among remaining people 5 – 3 + 1 Unit are = 3 !

And the 3 people unit can arrange among themselves in 3 ! ways.

So the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36

Total possible cases = 120 -36 = 84

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