a deli offers it's cheese sandwich with various combinations of mayo,lettuce, tomatoes, pickles and sprouts. 5 different types of cheese are avaiable. How many different chesse sandwiches are possible?
with the 5 condiments listed there would be 2^5 subsets or 32 different ways to have the condiments, including none and all of them
so the number of different sandwiches
= 32 x 5 ways
= 160
(this assumes that only one kind of cheese is on a sandwich.
If multiple cheeses can go on, there would be 2^10 -1 or 59048 ways to have the cheeses.
I subtracted 1 to exclude 'no cheeses'. Having a cheese sandwich without cheese is a contradiction.)