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Mathematics Elective 2 Exercise 3 after class (permutation and combination)
Let's see how many champions there are first. Because neither Party A nor Party B is a champion, there is C3 1.

Look at the last one. Because one person is already the first, and B is not the last one, there are still three people left, so the last one has C3 1.

Finally, look at 2 3 4 people, because some people are already the first and last, and there are still three people left, so there are A3 3 kinds.

So there are (c 31) * (c 31) * (a33) = 54 species.