Question

a restaurant offers the following limited lunch menu.
main courses beef, pork roast, duck, quiche
vegetables corn, green beans
beverages coffee, tea, milk, soda
desserts ice cream, brownies
if one item is selected from each of the four groups, in how many ways can a meal be ordered?
there are ways a meal can be ordered.

Explanation:

Step1: Count the number of choices for each group

Main Courses: \(4\) options (Beef, Pork Roast, Duck, Quiche)
Vegetables: \(2\) options (Corn, Green Beans)
Beverages: \(4\) options (Coffee, Tea, Milk, Soda)
Desserts: \(2\) options (Ice Cream, Brownies)

Step2: Apply the fundamental counting principle

The fundamental counting principle states that if there are \(m_1\) ways to do the first task, \(m_2\) ways to do the second task, \(m_3\) ways to do the third task, and \(m_4\) ways to do the fourth task, then the total number of ways to do all four tasks together is \(m_1\times m_2\times m_3\times m_4\).
Here, \(m_1 = 4\), \(m_2=2\), \(m_3 = 4\), \(m_4=2\)
So the total number of ways \(N=4\times2\times4\times2\)

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Answer:

\(64\)