A circular piece of paper is divided into five equal regions

A circular piece of paper is divided into five equal regions: We will consider how many ways we can color the paper, where each region is colored one color. How many ways can this piece of paper be colored using only black and white? (Again, only count colorings which yield distinct physical objects.) How many ways can it be colored with four colors? Give an example of a coloring showing why this answer is different than the answer to 7(f) above.

Solution

8(a) Ball can be covered in the following ways.

4 black 1 white + 3 black 2 white + 2 black 3 white + 1black 4 white = 5+4 +4+5 =18

(b) 4 colours can be arranged in 4! ways + 5 ways o arrange = 29 ways