elementary math for teachers
posted by jen .
A deli offers its cheese sandwich with various combinations of mayonnaise, lettuce, tomatoes,
pickles, and sprouts. 5 types of cheese are available. How many different cheese sandwiches are
possible?

the toppings on each sandwich can be done in 8 ways, the number of subsets of 3 elements. This will include the nullset, or no toppings.
The wording is not clear as to how many cheeses can go on a sanwich.
e.g. can you have a sandwich with 3 different cheeses?
I will assume we can only have one of the 5 cheeses, so the number of different sandwiches is 5(8) or 40.
If you can have any combination of cheese, there would be 2^5  1 or 31 ways to have just the cheese sandwich.
(I subtracted one to exclude the case of no cheeses. After all it is called a "cheese sandwich")
So in that case there would be 5(31) or 155 different sandwiches.
Your call.