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Mathematical permutation and combination problem
Answer 1: First choose 1 from three teachers, two from six students, then choose 1 from the remaining two teachers, and two from the remaining four students, and finally make a group. Obviously, the teachers are all arranged, so A33 should be excluded.

Answer 2: It doesn't make sense. This result doesn't make sense Three teachers choose 1 and six students choose 2. Who is the whole arrangement after that? You only choose one group, only choose one group. How do you arrange it?

Another solution: Teacher 3. 1 The teacher chooses two of the six students, the second teacher chooses two of the remaining four, and the third teacher chooses the remaining two. Results C62C42C22

It should be noted that,

Answer 1: All the teachers are arranged because they are all selected.

In another solution, teachers are not all arranged, although there seems to be a continuous allocation order.

Whether you can understand it depends on your own ability.