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[gatorPredent]

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how many arrangements can six people be seated around a circular table? Answer is a permutation problem, (n-1)!, but why isnt it 6!. My intuition tells me (6 different people)x(5 diff ")x(4")x(3")x(2")x(1") but thats not right. Any explanation to why my intuition is wrong would be awesome

 

[hunterpostbacst]

how many arrangements can six people be seated around a circular table? Answer is a permutation problem, (n-1)!, but why isnt it 6!. My intuition tells me (6 different people)x(5 diff ")x(4")x(3")x(2")x(1") but thats not right. Any explanation to why my intuition is wrong would be awesome

Imagine when six people sit around a circular table, you will find out that it's exactly same as they rotate to sit next to where they sat.

 

[gatorPredent]

still dont get it, would the answer be 6! if it were in a straight line how many ways can 6 people be arranged?

 

[UCB05]

still dont get it, would the answer be 6! if it were in a straight line how many ways can 6 people be arranged?

In a row, 1-2-3-4-5-6 is different from 4-5-6-1-2-3. the answer is 6!
But in a circle, -1-2-3-4-5-6- is the same as -2-3-4-5-6-1- is the same as -5-6-1-2-3-4- and cuts down the number of permutations possible, down to 5!