Required Mathematical Intelligence

Chapter 88 Pencils in Five Colors

There are five colors of pencils: red, yellow, blue, green, and white. Every two colors of pencils form a group. How many groups can be matched at most without repetition?

[Answer: Analysis and solution According to the meaning of the question, red pencils are matched with pencils of four colors: yellow, blue, green and white, and there are 4 groups without repetition; yellow pencils are matched with pencils of three colors of blue, green and white , there are 3 non-repeating groups; blue pencils are matched with green and white pencils respectively, and there are 2 non-repeating groups; green pencils and white pencils are matched, and there is 1 non-repeating group.So it can be matched into non-repeating 4 3 2 1=10 groups at most. ]
(End of this chapter)