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A combinatorial mathematics problem
First use intuitive analysis:

C(3, 1)=3

C(4,2)=6

The number 1-4 represents four different people, corresponding to the following situations respectively.

C(3, 1)=3 :( 12,34)、( 13,24)、( 14,23)

C(4,2)=6 :( 12,34)、( 13,24)、( 14,23)、(23, 14)、(24, 13)、(34, 12)

As can be seen, as group C (4,2) is repeated and not the correct answer.

In the same way; In a similar way

C(6,3)=20

C(5,2)= 10

Analysis reason: Because eight people are divided into three groups, there will be two groups with the same number of people. When dividing the two groups, we should not only eliminate those who meet this group, but also consider that the rest of the people have been eliminated, so the answer is:

C(4,2)/2 = 6/2 = 3 = C(3, 1)

C(6,3)/2 = 20/2 = 10 = C(5,2)

The answer in the book is to consider fixing one of the remaining two groups and then removing it from the rest.

This person, to complete this group, is:

C(4- 1,2- 1) = C(3, 1)

C(6- 1,3- 1) = C(5,2)