There are five sand which fillings - ham, cheese, tomato, lettuce and totally plain. How many combinations? I make 11.

Question

Ham, h & c, h & t, h&l; cheese, c & t, c & l; tomato; lettuce, l & t; sandwich with no filling. Total is 11. Some doubt in the family with this! Many thanks, William

Answer 1

A set of n elements has 2^n subsets, including the empty set.

So, if you have 4 fillings, and want at least one, that will allow for

2^4-1 = 15 different combinations, using 1 to 4 items.

add in the totally plain one, and that gives 16 ways to make the sandwich.

(not sand which!)