A juice bar allows customers to create a custom smoothie by selecting exactly 1 fruit base… — ACT

A juice bar allows customers to create a custom smoothie by selecting exactly $1$ fruit base out of $4$ available options and $1$ liquid base out of $3$ available options. How many different custom smoothie combinations of $1$ fruit base and $1$ liquid base are possible?

Answer: 12 combinations

Answer

The total number of possible smoothie combinations is 12.

According to the Fundamental Counting Principle, if there are

m

ways to make a first choice and

n

ways to make a second choice, there are

m \times n

total possible pairs. Here, multiplying

4

fruit choices by

3

liquid choices yields

4 \times 3 = 12

total smoothie combinations.

Step-by-Step Solution

Determine the number of options for each independent choice

Fruit base options = 4; Liquid base options = 3

Each choice is independent of the other.

Multiply the number of options for each choice using the Fundamental Counting Principle

4 x 3 = 12

To find the total number of combinations across multiple independent categories, multiply the number of choices in each category together.

Key Concept

Fundamental Counting Principle

Estimated Time:45s

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