https://file.aiquickdraw.com/mathbot/file/1725506611077az886n1i.jpg

The problem in the image asks about forming a committee from a pool consisting of:

- **10 Americans**
- **3 Australians**
- **7 Canadians**

The condition is that the committee must have equal representation from each country.

We need to determine how many people are there in the committee in total.

### Solution:

Since the committee must have equal representation from each country, the number of people selected from each country must be the same. The pool of people is:

- 10 Americans
- 3 Australians
- 7 Canadians

Since the smallest number of available people is **3 Australians**, the number of representatives from each country can only be **3** (because the Australians limit the size).

Thus, we choose:
- 3 Americans
- 3 Australians
- 3 Canadians

This forms a committee of **3 + 3 + 3 = 9** people.

### Correct Answer:
The committee will have **9** people.

Do you have any questions, or would you like more details?

### Related Questions:
1. What is the largest possible number of committee members if there is no requirement for equal representation?
2. How many ways can we select 3 representatives from 10 Americans?
3. What if the committee required at least 1 person from each country, what would the possibilities be?
4. How many committees could be formed if 5 members were required in total but with no restriction on equal representation?
5. How does the problem change if one more Australian joins the pool?

### Tip:
Always check for the limiting factor when equality is required in selections, especially when different groups have different total numbers.

A candidate pool for a committee has ten Americans, three Australians, and seven Canadians, and no one has multiple citizenships. If there are to be nine people on the committee and the committee must have equal representation of each country, how many ways are there to form the committee?

Learn how to solve a combinatorics problem involving forming a committee with equal representation from Americans, Australians, and Canadians. The solution explores proportional selection and the combination formula, suitable for students in Grades 9-12.

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