**Question:**

In one exam, Tran Quy Cap school had 12 students won prizes in which: $ 7 $ students won at least two prizes, $ 4 $ students won at least $ 3 $ prizes; $ 2 $ students won the most prize, each $ 4 $ prize. How many awards have A school won?

**Answer**

Call $ A, B, C, D $ in turn is a combination of students who won $ 4 $ prize, at least $ 3 $ prize, at least $ 2 $ prize and at least $ 1 $ prize. We have $ A \subset B \subset C \subset D $.

The number of students who have won the correct $ 4 $ prize is: $ 2 $

The number of students who correctly won $ 3 $ prize is: $ 4 – 2 = 2 $

The number of students who won the correct $ 2 $ prize is: $ 7 – 4 = 3 $

The number of students who won the correct $ 1 $ prize is: $ 12 – 7 = 5 $.

all:

$ 2.4 + 2.3 + 3.2 + 5.1 = 25 $ (prize).

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