Natalie has a choice of black blue or tan skirt to wear with a red blue or white sweater without calculating the number of possible outcomes how many more outfits can she add a yellow sweater to her collection
Answers
Step-by-step explanation:
Fundamental Counting Principle
Sometimes we want to know how many different combinations can be made of a variety of items. The fundamental counting principle states that the number of ways in which multiple events can occur can be determined by multiplying the number of possible outcomes for each event together. In other words, if events A, B, and C have 5, 3 and 4 possible outcomes respectively, then the possible combinations of outcomes is 5×3×4=60.
Let's solve the following problems.
Sofia works in a clothing store. She has been given the task of setting up a mannequin with a skirt, a shirt and a pair of shoes from a display of coordinating skirts, shirts and shoes. Since they all coordinate she can pick any shirt, any skirt and any pair of shoes and the outfit will work. If there are 3 skirts, 5 shirts and 2 pairs of shoes, how many ways can she dress the mannequin?
Let’s use a tree to help us visualize the possibilities. If we start with Shirt A, we get the following possibilities for the remainder of the outfit:

So we could have the following 6 combinations with Shirt A:
Shirt A, Skirt A, Shoe A
Shirt A, Skirt A, Shoe B
Shirt A, Skirt B, Shoe A
Shirt A, Skirt B, Shoe B
Shirt A, Skirt C, Shoe A
Shirt A, Skirt C, Shoe B
Consider that there are four other shirts that will also have 6 combinations of skirts and shirts that will go with them. Now, there are 5×6 total combinations which is 30 ways that Sofia could dress the mannequin.
Ralph is trying to purchase a new car. The salesperson tells him that there are 8 different possible interior colors, 5 exterior colors and 3 car models to choose from. How many different unique cars does he have to choose from?
Instead of making a tree diagram this time, let’s look at a more efficient method for determining the number of combinations. If we consider what happens in the tree diagram, the 8 different interior colors would each be matched with each of the 5 exterior colors and those combinations would then be linked to the 3 different models, we can see that:
8 interior colors×5 exterior colors× 3 models=8×5×3=120 combinations
Monique is having a 5 course dinner in the dining room on a cruise. The menu consists of 2 appetizers, 3 soups, 2 salads, 4 entrees and 3 desserts. How many different meals could be configured if she chooses one of each course?
Answer:
3 more outfits; She will have three different skirts that she can wear with the yellow sweater.
Step-by-step explanation: