Question

Determine whether a permutation, a combination, counting principles, or a determination of the number of subsets is the most appropriate tool for obtaining a solution, then solve. Some exercises can be completed using more than one method. A caterer offers eight kinds of fruit to make various fruit trays. How many different trays can be made using four different fruits?

Name: Problem 77, Chapter 10: Precalculus
Uploaded: 2020-05-24T16:27:21-08:00
Duration: 19 s
Channel: Elizabeth Xu
Description: Determine whether a permutation, a combination, counting principles, or a determination of the number of subsets is the most appropriate tool for obtaining a solution, then solve. Some exercises can be completed using more than one method. A caterer offers eight kinds of fruit to make various fruit trays. How many different trays can be made using four different fruits?

   Determine whether a permutation, a combination, counting principles, or a determination of the number of subsets is the most appropriate tool for obtaining a solution, then solve. Some exercises can be completed using more than one method.
A caterer offers eight kinds of fruit to make various fruit trays. How many different trays can be made using four different fruits?

Precalculus

John W. Coburn 2nd Edition

Chapter 10, Problem 77

Instant Answer

Solved by Expert Elizabeth Xu

05/24/2020

Step 1

The order in which the fruits are chosen does not matter, so this is a combination problem. Show more…

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Determine whether a permutation, a combination, counting principles, or a determination of the number of subsets is the most appropriate tool for obtaining a solution, then solve. Some exercises can be completed using more than one method. A caterer offers eight kinds of fruit to make various fruit trays. How many different trays can be made using four different fruits?

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Key Concepts

Permutations vs Combinations

This concept distinguishes between arrangements where order matters (permutations) and selections where order is irrelevant (combinations). Understanding the difference is crucial when determining the appropriate method to count outcomes in problems.

Combinations

Combinations involve selecting a subset of items from a larger set without regard to the order of selection. They are typically calculated using the binomial coefficient, which describes the number of ways to choose a specific number of items from a set.

Counting Principles

Counting principles, such as the fundamental counting principle, provide systematic methods to count the number of ways events can occur. They form the basis for more complex counting techniques and help determine which counting method (e.g., combinations or permutations) to apply in a problem.

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