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A senior high school math problem (permutation and combination)
Classmate A B C D

Greeting card 1 2 3 4

A2 B 1 C4 D3

A2 B3 C4 D 1

There are three situations when students A2 B4 C 1 D3 A take the exam 2. Similarly, there are three situations in A3 and A4.

So there are nine kinds of one * * *

Classmate A B C D E

Greeting card 1 2 3 4 5

A2 B 1 D3 E4 C5

A2 B1E3 C4 D5

A2 C 1 (not listed)

A2 D 1 (not listed).

A2 E 1 (not listed).

When a student gets 2, there are 8 situations. Similarly, there are 8 situations in A3, A4 and A5.

So there are 32 kinds of a * * *