
In a class, there are 15 boys and 10 girls. Three students are selected at random. What is the probability that all 3 are girls as a percent?

To solve this problem, we need to calculate the probability that all 3 selected students are girls, given that there are 15 boys and 10 girls in the class. 

### Step-by-step solution:

1. **Total number of students**:  
   The total number of students in the class is:  
   \[
   15 \, (\text{boys}) + 10 \, (\text{girls}) = 25 \, (\text{students})
   \]

2. **Total number of ways to select 3 students from 25**:  
   The number of ways to select 3 students from 25 can be calculated using the combination formula:
   \[
   \binom{25}{3} = \frac{25 \times 24 \times 23}{3 \times 2 \times 1} = 2300
   \]

3. **Number of ways to select 3 girls from 10**:  
   The number of ways to select 3 girls from 10 can also be calculated using the combination formula:
   \[
   \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120
   \]

4. **Probability that all 3 selected students are girls**:  
   The probability is the ratio of favorable outcomes (selecting 3 girls) to the total outcomes (selecting 3 students from the class):
   \[
   P(\text{all girls}) = \frac{\binom{10}{3}}{\binom{25}{3}} = \frac{120}{2300} = 0.05217
   \]

5. **Convert to percentage**:  
   To express the probability as a percentage, multiply by 100:
   \[
   0.05217 \times 100 = 5.217\%
   \]

### Final Answer:
The probability that all 3 selected students are girls is approximately **5.22%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the probability change if 4 students were selected?
2. What is the probability of selecting 2 boys and 1 girl?
3. What is the probability of selecting 3 boys?
4. How many different ways can 2 boys and 1 girl be selected?
5. What is the probability of selecting at least 1 girl?

**Tip**: When calculating probabilities involving selections, always consider using combinations when the order of selection does not matter.

In a class, there are 15 boys and 10 girls. Three students are selected at random. What is the probability that all 3 are girls as a percent?

Find the probability of selecting 3 girls from a group of 15 boys and 10 girls with a detailed step-by-step solution. Learn the combination and probability formulas used to solve this problem, suitable for students in Grades 8-10.

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