Math Problem Statement

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

Solution

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 = 5×3=155 \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 = 5×2=105 \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 = 3×2=63 \times 2 = 6

Total number of ways:

15+10+6=3115 + 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.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle

Formulas

Total combinations = Number of ways to choose from each group × Number of ways to choose from the other group

Theorems

Multiplication Principle of Counting

Suitable Grade Level

Grades 9-12