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
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!)
To find the number of combinations of sandwich fillings, you can use the concept of permutations. A permutation is an arrangement of items in a specific order. In this case, we want to find all the possible combinations of fillings for the sandwich.
First, let's list out all the possible fillings:
1. Ham
2. Cheese
3. Tomato
4. Lettuce
5. Totally plain (no filling)
To find the total number of combinations, we can use the formula for permutations with repetition. The formula is:
n^r
Where n represents the number of options and r represents the number of choices.
In this case, we have 5 options (fillings) and we are making a sandwich with 1 filling, 2 fillings, or no filling (3 choices).
To calculate the number of combinations:
1. Sandwich with 1 filling: 5^1 = 5 options
2. Sandwich with 2 fillings: 5^2 = 25 options
3. Sandwich with no filling: 5^0 = 1 option
Now, let's calculate the total number of combinations:
Total = Sandwiches with 1 filling + Sandwiches with 2 fillings + Sandwich with no filling
= 5 + 25 + 1
= 31
According to the calculations, there are 31 possible combinations of sandwich fillings.