Question

You are going to paint a six-sector spinner. There are 4 colors to choose from. How many different ways can you paint the spinner if each color can be used more than once and no two adjacent sectors can be the same color?

Answer 1

Using the Fundamental Counting Theorem, it is found that there are 648 ways to paint the spinner.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem, we have that the first sector can be painted in any of the 4 colors, the others until the 5th can be painted in 3 colors(not the adjacent), and the sixth in only 2, as it is adjacent to both the 5th and the 1st sectors, hence:

$n_1 = 4, n_2 = n_3 = n_4 = n_5 = 3, n_6 = 2$

Hence the number of ways is given by:

N = 4 x 3 x 3 x 3 x 3 x 2 = 648.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

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