Exercise 1 Page 938

a We are asked to find the number of possible lunches from the items shown in the given table.

Sandwich	Soup	Desert	Drink
chicken salad ham tuna roast beef	tomato chicken noodle vegetable	cookie pie	tea coffee cola diet cola milk

Let's calculate the number of items of each type.

	Sandwich	Soup	Desert	Drink
Items	chicken salad, ham, tuna, roast beef	tomato, $chicken noodle,$ vegetable	cookie, pie	tea, coffee, cola, diet cola, milk
Number of items	$4$	$3$	$2$	$5$

To calculate the number of possible lunches, we will use the Fundamental Counting Principle. According to this principle, the number of possible lunches is the product of all the numbers of items from the different types.

Different Lunches = 4 \cdot 3 \cdot 2 \cdot 5 = 60

We found that

60

different lunches can be created.

b We are asked to find the number of possible lunches if one soup and two desserts were added to the menu. To do that, let's add an example soup and two desserts to the menu!

Sandwich	Soup	Desert	Drink
chicken salad ham tuna roast beef	tomato chicken noodle vegetable $soup # 1$	cookie pie $dessert # 1$ $dessert # 2$	tea coffee cola diet cola milk

Just like in Part A, we will now calculate the number of items of each type.

	Sandwich	Soup	Desert	Drink
Items	chicken salad, ham, tuna, roast beef	tomato, $chicken noodle,$ vegetable, $soup # 1$	cookie, pie, $desert # 1,$ $desert # 2$	tea, coffee, cola, diet cola, milk
Number of items	$4$	$4$	$4$	$5$

To calculate the number possible lunches, we will use the Fundamental Counting Principle.

Different Lunches = 4 \cdot 4 \cdot 4 \cdot 5 = 320

If one soup and two desserts were added, then

320

different lunches could be created.

Subchapter links

Exercises p.938