Question

at a luncheon, there are different breads, meats, and cheeses to make sandwiches:
4 kinds of bread: wheat, rye, multi - grain, white
2 kinds of meat: ham, turkey
3 kinds of cheese: cheddar, swiss, provolone
if a sandwich has one kind of bread, one kind of meat, and one kind of cheese, how many different sandwiches can be made?
□ different sandwiches

Explanation:

Step1: Identify the number of choices for each component

We have 4 kinds of bread, 2 kinds of meat, and 3 kinds of cheese.

Step2: Apply the multiplication principle

The multiplication principle of counting 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.

So, the number of different sandwiches is \( 4\times2\times3 \).

Step3: Calculate the result

First, calculate \( 4\times2 = 8 \). Then, multiply this result by 3: \( 8\times3 = 24 \).

Answer:

24