Question

you go to the cafeteria for lunch and have a choice of 4 entrees, 5 sides, 5 drinks, and 4 desserts. assuming you have one of each category, how many different lunches could be made?

Explanation:

Step1: Identify the multiplication principle

To find the number of different lunches, we use the multiplication principle of counting, which states that if there are \(n_1\) ways to do one thing, \(n_2\) ways to do a second thing, \(n_3\) ways to do a third thing, and \(n_4\) ways to do a fourth thing, then the total number of ways to do all four things together is \(n_1\times n_2\times n_3\times n_4\).

Step2: List the number of choices for each category

• Number of entrees (\(n_1\)): 4
• Number of sides (\(n_2\)): 5
• Number of drinks (\(n_3\)): 5
• Number of desserts (\(n_4\)): 4

Step3: Apply the multiplication principle

Calculate the total number of different lunches by multiplying the number of choices for each category:
\[

$$\begin{align*} \text{Total number of lunches}&=n_1\times n_2\times n_3\times n_4\\ &= 4\times5\times5\times4\\ &= 4\times5 = 20; \quad 5\times4 = 20\\ &= 20\times20\\ &= 400 \end{align*}$$

\]

Answer:

400