Asked by will
There are five sand which fillings - ham, cheese, tomato, lettuce and totally plain. How many combinations? I make 11.
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
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
Answers
Answered by
Steve
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!)
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!)
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