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The problem involves a Venn diagram with three overlapping circles representing preferences for different sports among surveyed students:

- **H**: Hockey
- **S**: Soccer
- **F**: Football

The regions are marked with numbers representing the number of people who fall into each category. Here are the questions and how we would solve them based on this setup:

### Breakdown of Questions:
1. **Exactly one sport**:
   - Add the numbers in each section where only one sport is represented. 
   - These are the outer sections of each circle.

2. **All three sports**:
   - This is the intersection point of all three circles.

3. **Exactly two sports**:
   - Find sections where only two circles overlap (excluding the center overlap).

4. **Two specific sports, excluding another** (e.g., hockey and football, but not soccer):
   - Find the overlap between only the two requested circles.

5. **Did not prefer any sport**:
   - Subtract the total number of students who liked at least one sport from the total survey group.

I'll go through these calculations if you can confirm the total number of surveyed students. Please let me know if you’d like a detailed answer to each or have questions. 

### Related Practice Questions:
1. How many students preferred only hockey and no other sport?
2. What is the total number of students who preferred at least two sports?
3. If another sport was added, how would it affect the Venn diagram?
4. How can you calculate students who liked exactly one or exactly two sports only?
5. How would the diagram change if all students liked at least one sport?

### Tip:
For Venn diagrams with three circles, the most common mistake is overlooking the center section (all three groups). Always double-check this area in multi-set problems.

A survey asked students which team sport they preferred to watch. The results are in a Venn diagram with 'H' representing hockey, 'S' representing soccer, and 'F' representing football. Based on the diagram, answer the following questions:
(a) How many people preferred exactly one sport?
(b) How many people liked all three sports?
(c) How many people liked both hockey and football but not soccer?
(d) How many people liked at least one of the sports?
(e) If 900 people were surveyed, how many did not like any of the sports?

Solve a multi-set Venn diagram problem involving students' preferences for hockey, soccer, and football. Answer questions on the number of students who liked exactly one sport, all three sports, both hockey and football but not soccer, at least one sport, and those who liked none. Suitable for Grades 7-10.

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