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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.

 Dec 27, 2019
 #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 27, 2019
 #2
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I answered this question recently, or something very similar.  Try searching my answer.

 

 

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.

 

Here, I search for you, it was easy to find.

 

https://web2.0calc.com/questions/tricky-question_8

 

If you have the answer and were just looking for the method then please state what it is.

(Here and on the first one)

 Dec 27, 2019

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