number of ways to select two books from distinct subjects from 5 distinct computer books, three distinct math books,two distinct art books

To find the number of ways to select two books from distinct subjects, we first need to calculate how we can choose books from different subject groups (Computer, Math, and Art).

### Breakdown:

- There are 5 distinct Computer books.
- There are 3 distinct Math books.
- There are 2 distinct Art books.

The selection must be from different subjects, so we need to consider the following combinations of subject pairs:

1. **One Computer book and one Math book:**
   - Ways to select one Computer book = 5
   - Ways to select one Math book = 3
   - Total ways for this pair = \( 5 \times 3 = 15 \)

2. **One Computer book and one Art book:**
   - Ways to select one Computer book = 5
   - Ways to select one Art book = 2
   - Total ways for this pair = \( 5 \times 2 = 10 \)

3. **One Math book and one Art book:**
   - Ways to select one Math book = 3
   - Ways to select one Art book = 2
   - Total ways for this pair = \( 3 \times 2 = 6 \)

### Total number of ways:
\[
15 + 10 + 6 = 31
\]

Thus, the total number of ways to select two books from distinct subjects is **31**.

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Here are 5 related questions to expand on this topic:

1. How would the solution change if there were more distinct subjects?
2. What if we had to select three books from distinct subjects?
3. How many ways are there to select two books from the same subject?
4. How many ways can we select one book from each subject?
5. What if one subject must always be chosen?

**Tip:** When selecting from distinct groups, combinations often involve multiplying the individual choices from each group.

Number of ways to select two books from distinct subjects from 5 distinct computer books, three distinct math books, and two distinct art books.

Explore how to find the total number of ways to select two books from distinct subjects in this combinatorics problem. Given 5 distinct computer books, 3 distinct math books, and 2 distinct art books, the solution covers key counting principles and multiplication rule. Suitable for students in Grades 9-12.

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