Now, Tosin doesn't care about the order of the ingredients in her sandwich. After all, it's all going to the same place. Therefore, any order is considered the same as long as the same ingredients are used (and the same total number of ingredients are used).
So, a sandwich that, from the bottom up, has lettuce, cheese, and tomato is the same as one that has cheese, tomato, and lettuce or tomato, cheese, and lettuce.
When the order doesn't matter, we refer to the set of components as a combination, rather than a permutation. Tosin wants to know how many unique sandwiches she can make. Because she doesn't care about the order of ingredients, she is trying to determine the number of combinations of ingredients she can have.
There are two types of combinations. Can you think of what those two types might be?
The two types of combinations are ones in which repetition is allowed and ones in which repetition isn't allowed, just like the two types of permutations.
Although combinations differ from permutations in fundamental ways, the two do share some similarities.
Question
Since Tosin doesn't care about the order of her ingredients, do you think she'll be able to make more or fewer unique sandwiches (compared to the number of sandwiches she could make if she did care)?
