Question

1. a sandwich shop offers 3 types of bread, 4 kinds of meat, and 2 kinds of cheese. how many different sandwiches can be made with one kind of bread, one kind of meat, and one kind of cheese? a. 9 b. 12 c. 24 d. 30

Explanation:

Step1: Identify the counting principle

We use 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, \(m = 3\) (types of bread), \(n = 4\) (kinds of meat), and \(p = 2\) (kinds of cheese).

Step2: Apply the multiplication principle

Calculate the total number of different sandwiches by multiplying the number of options for each component: \(3\times4\times2\). First, \(3\times4 = 12\), then \(12\times2 = 24\).

Answer:

c. 24