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Question

Difficulty: EasyPermutations, Combinations, and Fundamental Counting Principle

A bookshelf holds 44 distinct fiction novels and 33 distinct non-fiction books. If a reader chooses exactly 11 fiction novel and 11 non-fiction book to take on a trip, how many different pairs of books can the reader select?

Answer: 12 pairs

Answer

The total number of different pairs of books that can be selected is 1212.
According to the Fundamental Counting Principle, if one task can be performed in mm ways and a second task can be performed in nn ways, the two tasks together can be performed in m×nm \times n ways. Choosing a fiction novel (44 options) and a non-fiction book (33 options) results in 4×3=124 \times 3 = 12 unique pairs.

Step-by-Step Solution

1
Determine the number of ways to choose one fiction novel
There are 44 possible choices.
The shelf contains 44 distinct fiction novels.
2
Determine the number of ways to choose one non-fiction book
There are 33 possible choices.
The shelf contains 33 distinct non-fiction books.
3
Calculate total pairs using the Fundamental Counting Principle
4×3=124 \times 3 = 12
The selection of a fiction novel and a non-fiction book are independent decisions, so the number of outcomes is the product of the number of choices for each decision.

Key Concept

Fundamental Counting Principle
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Topics

Permutations, Combinations, and Fundamental Counting Principle

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