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MrRoyal

There are 258 ways to color the octagon such that no two adjacent vertices are the same color

How to determine the number of ways?

The given parameters are:

  • Sides, n = 8 --- the sides of an octagon
  • Colors, r = 3 i.e. red, green and blue

Since no two adjacent vertices are the same color, we use the following  chromatic polynomial of an octagon equation

Ways = (r - 1)⁸ + (r -1)

Substitute 3 for r

Ways = (3 - 1)⁸ + (3 -1)

Evaluate

Ways = 258

Hence, there are 258 ways to color the octagon

Read more about combination at:

https://brainly.com/question/11732255

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