a We are told that a hotel restaurant serves omelets with the following choices.
Omelet Options
Side Options
Vegetable Omelet
Hash Browns
Sausage Omelet
Grits
Ham Omelet
Toast
Choosing a vegetable omelet has additional options for vegetable choices.
Green peppers
Tomatoes
Onions
Mushroom
We will find the number of different outcomes of omelets and one side if a vegetable omelet choice comes with just one vegetable. To do so we will use the Fundamental Counting Principle. Let's first recall the principle.
Fundamental Counting Principle
If an event A has n possible outcomes and an event B has m possible outcomes, then the total number of different outcomes for A and B combined is n * m.
Since choosing vegetable omelets has extra choices, we will find the number of outcomes of choosing vegetable omelets and the number of outcomes choosing the other types of omelets. Then we will add the results to find the desired number of outcomes.
Number of Outcomes of Choosing the Omelet Types
Number of Outcomes of Choosing the Side
Number of Outcomes of Choosing One Vegetable
Fundamental Counting Principle
Choosing Vegetable Omelet
1
3
4
1* 3 * 4=12
Choosing Another Type of Omelet
2
3
-
2* 3=6
Now we will add the results to find the number of different outcomes of omelets and one side when a vegetable omelet choice comes with just one vegetable.
12+6=18
b In this exercise we will find the number of possible outcomes for choosing a vegetable omelet if we get any or all vegetables on any omelet. We will use the Fundamental Counting Principle. Notice that we have five options for vegetable choices — green peppers, tomatoes, onions, mushrooms, or all vegetables.
Number of Outcomes of Choosing the Side
Number of Outcomes of Choosing Vegetables
Fundamental Counting Principle
Choosing Vegetable Omelet
3
5
3 * 5=15
There are 15 possible outcomes to choose a vegetable omelet if we get any or all vegetables on the omelet.
