Suppose four people are A, B, C, D, three categories are A, B, C, and A has been fixed as Class A, and there are three situations:

If there are two students in Class A, there are 3×2=6 kinds of * * *;

If Class B is divided into two people, there are three kinds of * * *;

If the class is divided into two people, there are three kinds of * * *;

In a word, four students are assigned to three classes. Student A must go to Class A, with at least one person in each class. * * * There are 6+3+3 = 12 arrangements.

Extended data:

This problem is a combination problem. Taking any m(m≤n) elements among n different elements as a group is called taking out the combination of m elements from n different elements.

The total number of combinations is a positive integer, which refers to the sum of all combinations of 0, 1, 2, …, n different elements taken out from n different elements at one time, that is

The total number of combinations of a group of n elements is the number of its subsets. The properties of the combination number formed by taking out M different elements from N different elements at one time are as follows:

1、

2、

Using these two properties, we can simplify the calculation of combination number and prove the problems related to combination number.