Let's analyze the Venn diagram and answer the questions:

Given Information:

• The Venn diagram shows the survey results for 649 people.
• Each number in the Venn diagram represents how many people fall into each category.

Step-by-Step Analysis:

1. People who own exactly one type of animal:

   • These are the people who are in only one category:
     • Own only a fish: $47$
     • Own only a cat: $38$
     • Own only a bird: $102$
   • Total for exactly one type: $47 + 38 + 102 = 187$.

   Answer (a): 187 people.

2. People who own a cat (including all combinations that involve a cat):

   • Own only a cat: $38$
   • Own a cat and a fish: $135$
   • Own a cat and a bird: $54$
   • Own all three: $68$
   • Total owning a cat: $38 + 135 + 54 + 68 = 295$.

   Answer (b): 295 people.

3. People who own both a bird and a fish, but don’t own a cat:

   • This category is represented by the number $123$ in the Venn diagram.

   Answer (c): 123 people.

Let me know if you have questions or need a deeper explanation!

Here are 5 related questions you might find interesting:

1. How many people own a fish?
2. How many people own both a cat and a bird, but not a fish?
3. How many people own at least one type of animal?
4. How many people own exactly two types of animals?
5. How many people do not own any pets?

Tip: Venn diagrams are a great tool for visualizing and solving problems involving sets and overlaps!