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Several permutation and combination problems
1. If one is removed from each class, it is equivalent to allocating two places to eight classes.

Type 1: Every class has 1, so c82=28.

Type 2: 1 Class has 2 classes, then c8 1=8.

Total ***28+8=36 species.

2. Always play the national anthem 8 times.

China and Greece are in harmony, and the Stars and Stripes are excluded by insertion.

The rest are 2 China, 1 Japanese, a total of 4 combinations.

Then insert two Americans into five of them, and the total is p44*p52=480.

3. I. Otsuichi Group, p22

C and d are similar to the last question about the United States, so let's rule it out first.

The remaining groups A, B and E are p22.

Insert c and d into three intermediate positions, p32.

Total ***p22*p22*p32=24 species.

The idea of this problem is: arrange 9 people-A at the head-B at the tail +A at the head and B at the tail.

So P99-P88-P88+P77 = 287,280 species.