Question

the lunch special at gregs restaurant is a sandwich, a drink and a dessert. there are 3 sandwiches, 1 drink, and 3 desserts to choose from. how many lunch specials are possible?

Explanation:

Step1: Identify the counting principle

This is a problem of counting the number of possible lunch specials by multiplying the number of choices for each component (sandwich, drink, dessert) using the multiplication principle of counting. The multiplication principle 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 sandwich choices \(m = 3\), the number of drink choices \(n=1\), and the number of dessert choices \(p = 3\).

Step2: Apply the multiplication principle

We calculate the total number of lunch specials by multiplying the number of choices for each category: \(3\times1\times3\).
First, multiply \(3\times1=3\). Then, multiply the result by \(3\): \(3\times3 = 9\).

Answer:

\(9\)