Question

introduction to the counting principle the lunch special at deandres restaurant is a sandwich, a drink and a dessert. there are 2 sandwiches, 3 drinks, and 2 desserts to choose from. how many lunch specials are possible?

Explanation:

Step1: Identify the counting principle

This problem uses the multiplication principle of counting, which states that if there are \( m \) ways to do one thing, \( n \) ways to do a second thing, and \( p \) ways to do a third thing, then there are \( m\times n\times p \) ways to do all three things together. Here, the number of ways to choose a sandwich is \( 2 \), a drink is \( 3 \), and a dessert is \( 2 \).

Step2: Apply the multiplication principle

To find the total number of lunch specials, we multiply the number of choices for each component: \( 2\times3\times2 \).

First, calculate \( 2\times3 = 6 \). Then, multiply this result by \( 2 \): \( 6\times2 = 12 \).

Answer:

\( 12 \)