C of two kinds of clothes stands for choosing two kinds of clothes that don't repeat from four kinds, and A stands for children to choose one from two kinds of clothes. Because there are only two colors in this method, the first child chooses one color, and the colors of other children must be fixed.

Four colors are also easy to understand. The first child chooses one of the four colors, the second chooses one of the remaining three colors, the third chooses 1, and the last one is fixed. It can be obtained directly by using a44.

The hardest thing is to choose three colors. At this time, it is best to assume that there are four children in a circle, abcd.

Adjacent colors can't be the same, so ac can have a group of colors the same, and bd can also have a group of colors the same, which is the origin of multiplying by 2.

4 Choose three colors without repetition, and four colors can be calculated by c43.

In addition, a33 regards ac as a whole (A changes color, C changes color), and then considers that the colors of ac.b and D can have different changes, so a33 can be used in six combinations.

A22 should not exist. It should be calculated by the initial multiplication of 2, and 2 times c43 times a33 is exactly 48. The formula is wrong, but the result is correct. It should be wrong.