Question

Difficulty: EasyBasic Probability and Counting Methods

A cafe offers a lunch special where a customer selects $1$ sandwich from $4$ available options, $1$ side dish from $3$ available options, and $1$ drink from $5$ available options. How many different total lunch combinations consisting of one sandwich, one side dish, and one drink can a customer choose?

Answer: 60 combinations

Answer

60 combinations

According to the Fundamental Counting Principle, if one event can occur in

m

ways, a second in

n

ways, and a third in

p

ways, the total number of combinations for all three events occurring together is

m \times n \times p

. Multiplying

4

sandwiches by

3

sides by

5

drinks yields

4 \times 3 \times 5 = 60

distinct lunch combinations.

Step-by-Step Solution

1

Identify the number of options available for each independent selection.

4 sandwiches, 3 side dishes, 5 drinks

The total outcomes depend on making one selection from each distinct category.

2

Apply the Fundamental Counting Principle.

4 × 3 × 5 = 60

The total number of outcomes for independent sequential choices is the product of the number of options for each choice.

Key Concept

Fundamental Counting Principle

Estimated Time:45s

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Topics

Basic Probability and Counting Methods

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