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*3*2*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*4*4*5=320
If one soup and two desserts were added, then 320 different lunches could be created.
