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What are the extracurricular math groups?
(1) According to the meaning of the question, one of the 34 people is required to be the person in charge.

That is, there are C34 1=34 selection methods;

(2) According to the meaning of the problem, it is divided into four steps.

In the first, second, third and fourth steps, a student is selected from 1 class, class 2, class 3 and class 4 as the group leader respectively.

Therefore, * * * has different selection methods: N=7×8×9× 10=5040 (species).

(3) According to the meaning of the question, it is discussed in six situations.

① Choose 1 student from Class One and Class Two, with 7×8 different selection methods;

② Select 1 student from Class 1 and Class 3 respectively, and adopt 7×9 different selection methods.

③ Choose 1 student from Class One and Class Four respectively, and there are 7× 10 different ways to choose;

④ 65,438+0 students were selected from Class Two and Class Three respectively, with 8×9 different selection methods;

⑤ Choose 1 student from Class Two and Class Four, and there are 8× 10 different choices;

⑥ Choose 1 student from Class Three and Class Four, with 9× 10 different selection methods.

Therefore, * * has different selection methods: n = 7× 8+7× 9+7×10+8× 9+8×/kloc-0+9×10 = 431(species).