Chipotle Combinations

Why I like this problem: This problem can be used as an introduction to combinations and permutations, or simply as a brain teaser. I like that students needed to think about the possible combinations in an organized manner and keep track of the meals they had accounted for to avoid counting them multiple times. Students are also easily able to connect with the problem since they all know the fast food chain. 

Observations from class: Students easily figured out that there are 24 possible variations of the major options (type of meal and "meat"), but slowed down when they reached the toppings. I could tell that they would become frustrated with the amount of options they had for the toppings, so I tried to hint to them that "only taking one topping" and "leaving out only one topping" were essentially the same thing probability-wise and would have the same number of outcomes. Some students also struggled to understand why order of toppings did not matter in this case, and how this affected their answer. 

Follow-up questions I asked: 

1. How many more possibilities do you have if you put multiple salsas or mix the meat options?
2. What do you notice about using 13 vs 1 of the topping offered? What about 12 vs 2? Etc.
3. How would the meal possibilities change if the restaurant allowed multiple servings of the same toppings?

Required skills / content: Combinations, permutations, systematic organization. 

Links: PDF 

Source: https://www.yummymath.com/