Asked 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?

Answers

Answered by Reiny
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.
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions