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5 Noble Knights are to be seated at a round table. In how many ways can they be seated?

A)120 B)96 C)60 D)35 E)24

(5-1)!= 4! = 24
Circular permutation formula is (n-1)!
This is solved by taking one knight in a fixed position and you have 4! ways to arrange the remaining 4.

good variation of this problem: how many ways can you seat 5 girls and 5 boys around a circular table if the girls and boys should alternate?

Is the answer 576?

The ways to seat 5 girls around the table = 24 The ways to seat 5 boys around the table = 24

24 x 24 = 576

Is that right?

The way I see it is as follows:

Say we pick one of the girls (everything else will revolve around her)
Number of ways to arange 5 girls is 24. Boys go in between so they can be seated in 5! ways. I'm sticking with my answer, but would like to see what other people think.

I think 24*24 is right. The rules of circular permutation still applies. We have basically two circles: one circle of boys and one circle of girls. Thoughts?

leeye84, hope the other explanations have made it clear why (n-1)! is used for the roundtable pizza party

hayabusa, good thinking!
your answer is correct for the second problem - only need to fix one of them from one of the groups - the second group can be arranged in the regular way - hence n! * (n-1)! is the OA

leeye84, hope the other explanations have made it clear why (n-1)! is used for the roundtable pizza party

hayabusa, good thinking! your answer is correct for the second problem - only need to fix one of them from one of the groups - the second group can be arranged in the regular way - hence n! * (n-1)! is the OA

That's exactly what I said! The second group (say the boys is 5!) The first is (5-1)! - cause we rotate around one of the chicks. Ans is 4!*5!

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