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The question provided in the image asks:

**"There are 6 girls and 4 boys running a race. What is the probability that only boys will finish in the top three places?"**

Let's solve this step by step:

### 1. Total number of participants:
- There are 6 girls and 4 boys, so a total of \(6 + 4 = 10\) participants.

### 2. Ways to choose 3 boys to finish in the top three:
- Since we want only boys to finish in the top three, we are choosing 3 boys out of the 4 available boys.
- The number of ways to arrange 3 boys out of 4 is the number of **permutations** of 4 boys taken 3 at a time, which is:
  \[
  P(4, 3) = \frac{4!}{(4-3)!} = 4 \times 3 \times 2 = 24
  \]

### 3. Total possible outcomes for the top three places:
- We can select any 3 participants out of the total 10 participants for the top three places.
- The number of ways to arrange 3 participants from 10 is the number of permutations of 10 taken 3 at a time:
  \[
  P(10, 3) = \frac{10!}{(10-3)!} = 10 \times 9 \times 8 = 720
  \]

### 4. Probability that only boys finish in the top three:
- The probability is the ratio of favorable outcomes (boys in the top three) to the total possible outcomes:
  \[
  \text{Probability} = \frac{P(4, 3)}{P(10, 3)} = \frac{24}{720} = \frac{1}{30}
  \]

Thus, the probability that only boys will finish in the top three places is **\(\frac{1}{30}\)**.

### Answer: \( \boxed{\frac{1}{30}} \)

Let me know if you would like further details or have any questions! Here are five related questions you might find interesting:

1. What is the probability that at least one girl finishes in the top three places?
2. How does the probability change if there are 5 boys and 5 girls in the race?
3. What is the probability that exactly 2 boys and 1 girl finish in the top three?
4. How would the calculation change if we only cared about who wins first place (not the top three)?
5. How do you calculate the number of combinations if order doesn't matter?

**Tip**: When calculating permutations, remember that the order in which participants are arranged matters. If order doesn't matter, you would use combinations instead of permutations.

There are 6 girls and 4 boys running a race. What is the probability that only boys will finish in the top three places?

Learn how to calculate the probability that only boys will finish in the top three places in a race with 6 girls and 4 boys. This problem involves the permutation formula and is suitable for high school students in Grades 9-12.

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