Answer these questions independently of each other
10 students took a test and each one got the distinct score. In how many ways can three distinct prizes be given?

Options

A. 270
B. 360
C. 720
D. 540

Answer

To solve the problem of how many ways three distinct prizes can be awarded to 10 students who have distinct scores, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Students**:
We have 10 students.

2. **Determine the Positions for Prizes**:
We need to award three distinct prizes: 1st, 2nd, and 3rd.

3. **Choose the Recipient for the 1st Prize**:
For the 1st prize, we can select any of the 10 students. Therefore, there are 10 choices.

4. **Choose the Recipient for the 2nd Prize**:
After awarding the 1st prize, only 9 students remain eligible for the 2nd prize. Thus, there are 9 choices for the 2nd prize.

5. **Choose the Recipient for the 3rd Prize**:
After awarding the 2nd prize, only 8 students remain eligible for the 3rd prize. Therefore, there are 8 choices for the 3rd prize.

6. **Calculate the Total Number of Ways to Award the Prizes**:
To find the total number of ways to award the three distinct prizes, we multiply the number of choices for each prize:
\[ \text{Total Ways} = 10 \times 9 \times 8 \]

7. **Perform the Calculation**:
\[ 10 \times 9 = 90 \]
\[ 90 \times 8 = 720 \]

8. **Conclusion**:
Therefore, the total number of ways to award the three distinct prizes is 720.

### Final Answer:
The total number of ways to give three distinct prizes to 10 students is **720**.