Solve by applying Polyas Theorem A new manufactured pencil d

Solve by applying Polya\'s Theorem:

A new manufactured pencil divided into 8 equal segments each of which is to be colored. How many ways can this be done if 3 colors are availbe?

Solution

By Polya\'s Enumeration therorem, mⁿ is the number of ways to color n objects with m colors.

In this problem m =3 and n= 8 so number of ways the pencil can be colored is 3⁸ = 6561