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Lance has a regular heptagon (7-sided figure). How many distinct ways can he label the vertices of the heptagon with the letters in OCTAGON if the N cannot be next to an O ? Rotations of the same labeling are considered equivalent.

 

I'm not sure how to solve this.

 Dec 23, 2019

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 #1
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There are 7! = 5040 ways to label the heptagon.  There are 4! = 24 ways where the O's are next to an N, so the number of ways where N is not next to an O is 5040 - 24 = 5016.

 Dec 23, 2019
 #2
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There are 7!/7 ways to label a heptagon, not 7! . You are overcounting.

Guest Dec 27, 2019

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