https://file.aiquickdraw.com/mathbot/file/1728357492275zb20y8rh.jpg

The problem is in Japanese and translates to:

**Problem 5:**
There are 9 members in the soccer club, 9 members in the swimming club, and 7 members in the judo club. When selecting 3 members randomly from these, what is the probability that all three come from different clubs? Round off to the nearest whole number and give the answer as a percentage.

### Solution:
1. **Total number of students**: \( 9 + 9 + 7 = 25 \)

2. **Total number of ways to select 3 students**:
   \[
   \text{Total ways} = \binom{25}{3} = \frac{25 \times 24 \times 23}{6} = 2300
   \]

3. **Number of ways to select 3 students such that each is from a different club**:
   - We need to select 1 from each club: 1 from soccer, 1 from swimming, and 1 from judo.
   - The number of ways to do this is:
     \[
     9 \times 9 \times 7 = 567
     \]

4. **Probability that all 3 students are from different clubs**:
   \[
   \text{Probability} = \frac{567}{2300} \approx 0.24652
   \]
   Converting this to a percentage:
   \[
   0.24652 \times 100 \approx 24.65
   \]
   Rounding this to the nearest whole number:
   \[
   \approx 25\%
   \]

So, the probability that the three selected students are all from different clubs is **25%**.

Would you like a more detailed explanation or have any questions about this problem?

### Related Questions:
1. How do you calculate combinations like \(\binom{n}{r}\)?
2. What is the difference between permutations and combinations?
3. How do probabilities change if we change the number of members in each club?
4. What is the general formula for calculating probabilities when selecting items from multiple groups?
5. How can rounding affect the accuracy of probabilities in calculations?

### Tip:
When dealing with probability problems involving multiple groups, always start by calculating the total possible outcomes and the desired outcomes separately before dividing them.

サッカー部9人、水泳部9人、柔道部7人からランダムで3人を選んだ時、3人がすべて違う部活になる確率は何％か。小数点以下第1位を四捨五入して整数のみで答えよ。

Learn how to calculate the probability of randomly selecting students from different clubs. This problem involves 9 soccer players, 9 swimmers, and 7 judo members. We explore combinatorics and probability to solve the problem step-by-step. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation