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Question

Difficulty: EasyCounting Principles

A military dining facility offers 55 different main courses, 33 different side dishes, and 44 different beverages. If a standard meal consists of exactly one main course, one side dish, and one beverage, how many different meal combinations can be chosen?

  1. A
    12
  2. B
    19
  3. 60Answer
  4. D
    20

Answer

There are 6060 different meal combinations possible.
The correct answer is 6060. According to the Fundamental Counting Principle, when there are multiple independent choices to be made to form a single outcome, the total number of combinations is found by multiplying the number of options for each choice. Here, we multiply the 55 main courses by the 33 side dishes and the 44 beverages: 5×3×4=605 \times 3 \times 4 = 60 possible meal combinations.

Step-by-Step Solution

1
Identify the number of available choices for each part of the meal.
Main courses = 55, Side dishes = 33, Beverages = 44.
The Fundamental Counting Principle requires knowing the total number of options for each independent selection stage.
2
Apply the Fundamental Counting Principle by multiplying the choices together.
5×3×45 \times 3 \times 4
When selections are made in sequence and are independent of one another, the total number of combinations is the product of the number of options at each individual step.
3
Calculate the final product.
6060
Multiplying the choices yields the total possible unique meal combinations.

Key Concept

Fundamental Counting Principle
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Topics

Counting Principles

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