As for the method to paint A to D by using all four colors of red, blue, yellow and white to distinguish the border of A,B,C,D in the figure below, how many ways are there?
Answer
Because the color to paint B is chosen one color among three colors except one color that painted in A, it is three ways.
Because the color to paint C is chosen one color among two colors except two colors painted in A and B, it is two ways.
Because the color to paint D is one color that remained last, it is one way.
Therefore, it is 4 × 3 × 2 × 1 = 24 ways in total.
24 ways
Solution
The color to paint A is four ways by choosing one color among four colors.
Because the color to paint B is chosen one color among three colors except one color that painted in A, it is three ways.
Because the color to paint C is chosen one color among two colors except two colors painted in A and B, it is two ways.
Because the color to paint D is one color that remained last, it is one way.
Therefore, it is 4 × 3 × 2 × 1 = 24 ways in total.
