In the grouping problem, if there are n groups with the same number of people, there will be repeated calculations, so it is necessary to use Ann to divide and remove the repeated parts.

Look at a simple example. There are four people in ABCD, divided into two groups on average.

According to the algorithm, it should be: C24 × C22 = 6.

According to the above algorithm, two people are randomly selected from four people and divided into one group, and the remaining two people are divided into one group. So if the two people who are separated first are A and B, and the rest are C and D, this is a situation. The same is true if C and D are grouped and A and B remain as a group. In fact, the above two cases belong to the possibility of grouping (AB, CD), and if calculated by C24 × C22, they are calculated as two kinds. In addition, (AC, BD) is equivalent to (BD, AC), and (AD, BC) is equivalent to (BC, AD). So there are six kinds calculated above, but actually there are only three kinds.

The root cause of this problem is that once the number of people divided into N groups is the same, the members of these N groups will still be the same after exchanging with each other, but according to the original algorithm, it is a different situation. But all possible situations in which n groups exchange with each other are Ann, so the calculated value is Ann times the real value, so it should be divided by Ann.

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