We hear the word combination all the time in everyday life. It's used to describe sequences for opening lockers, mixtures of flavors, and the application of different perspectives (e.g., combined intellect/combined forces).
However, in mathematics, a combination is something much more specific. For instance, in mathematics, there are distinctions between permutations and combinations. We can also use formulas to calculate the number of combinations possible in a particular situation.
For example, Tosin runs the best deli in Combinator County. She's been having a great year and decides that she wants to make the best sandwich the town's ever seen. She has a number of ingredients available to her, and she wants to know how many unique sandwiches she can make with these ingredients.
Now, we already know how to calculate permutations from an earlier lesson. But, in this case, it makes more sense to calculate the number of different combinations Tosin can make. In order to help her figure this out, we will learn what makes a combination a combination. We'll also learn how to calculate the number of combinations that exist given certain parameters.
Question
Both combinations and permutations can be represented as events that require decisions to be made. Can you recall the principle that allows us to determine the number of possible outcomes in an event given the number of decisions and choices available to those decisions?
