Question

a restaurant offers the following limited lunch menu.
main courses beef, pork roast, duck, quiche
vegetables broccoli, carrots, potatoes
beverages coffee, tea, milk, soda, shakes
desserts cake, pie, sherbet
if one item is selected from each of the four groups, in how many ways can a meal be ordered?
there are \boxed{} ways a meal can be ordered.

Explanation:

Step1: Count the number of choices for each category

• Main Courses: \(4\) options (Beef, Pork Roast, Duck, Quiche)
• Vegetables: \(3\) options (Broccoli, Carrots, Potatoes)
• Beverages: \(5\) options (Coffee, Tea, Milk, Soda, Shakes)
• Desserts: \(3\) options (Cake, Pie, Sherbet)

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, \(m_1 = 4\), \(m_2=3\), \(m_3 = 5\), \(m_4=3\)

$$
LATEXBLOCK0
$$

Answer:

\(180\)