Question: 6 adults and 3 children are sitting in a round table. Find the number of possible seating arrangement if none of the children sit together.

Solution: Choose 3 out of the 6 possible slots for the children to be seated between 2 adults, then multiply by 3! for the children permutation, then multiply by (6-1)! for the 6 adult circular permutation. Ans: 14400

Principle used: Slotting principle.

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Hi, for this question why can’t I take 6C3 or even 6P3 since there is 6 slots for the children to choose from? I don’t understand why it is 3!

Yes, you can. What I did was 6C3 x 3!

They are the same since 6P3= 6C3 x 3!

Oh yes, thanks for clarifying my doubt. 🙂