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Multiplication principle of Olympic mathematics problems in primary schools
The first case: the prizes for four people are different.

5*4*3*2= 120

The first person chooses one of the five prizes for him, so the second one has only four choices, the third one has three, and the second one has two.

The second case: there are two people who share the prize. Then use three prizes.

3 out of 5 cases had 10 cases. The distribution of 4 people is 12.

10* 12= 120

The third case: only two kinds of prizes are used.

10*2=20

Total * * * "120+120+20 = 260.