A (upper 4, lower 4) is to arrange all four classes.
Because of special circumstances, the Chinese teacher should be subtracted from the first class and the math teacher should be subtracted from the fourth class.
In the first class, the Chinese teacher's situation is A (upper 3 and lower 3).
In the fourth class, the math teacher has a (upper 3, lower 3)
Why do you want to add a (up 2 and down 2)? Because there is a repetition when the Chinese teacher is subtracted from the first class or the math teacher is subtracted from the fourth class, that is, the Chinese teacher is arranged for the first class and the math teacher is arranged for the fourth class.
2. In the answer given, A (7 in both directions) means that all seven people will be ranked.
Because Party A and Party B can't be together, we should subtract the fact that they are together.
What's the situation when A and B line up together? If A and B are tied together, this time it is equivalent to arranging all six people, so it is A (6 up and down).
Then why multiply it by 2? Because there is a side-by-side arrangement of A and B, it is A (both up and down are 2).
3. The topic is wrong. It should be a triangular pyramid with the vertex of a cuboid as the vertex.
A cuboid has eight vertices, and four of them are selected, so there is C (lower 8, upper 4).
However, if the four selected points are on the same plane, it is not a triangular pyramid. There are 12 kinds of this situation, but you can't think of 12 kinds.
6 faces and 6 diagonal faces
4, less than 50000, naturally the first number can't be 5; Even number, so the last one is 2 or 4.
So: If it is an even number, the last position is C (upper 1, lower 2).
The first position can't be 5, and the last position is 1, so there are still 3 numbers (excluding 5), so the first position has a c (up 1, down 3).
The head and tail positions are arranged, and the other three numbers (including 5) are arranged in the middle three positions, so it is a (up and down 3).
So the synthesis is: c (upper 1 and lower 2)×C (upper 1 and lower 3)×A (upper 3 and lower 3) = 2× 3× 3 = 36.