how many different combination sandwichs can be made from 3 different breads, 5 different meats and 4 cheese

Answer 1

Assuming a sandwich has two slices of bread and any possible combination of meat and cheese fillings the answer is 3072.
Lets say the bread types are A, B, and C.
you could use 2A's, 2 B's, 2 C's, AB, AC, or BC for the bread slices. Thats 6 combinations.
For the meat, there are 2^5 or 32 combinations. Thats C(5,0) + C(5,1) + C(5,2) + C(5,3) + C(5,4) + C(5,5) where C(a,b) is the combination of a things taken b at a time.
For the cheese, there are 2^4 or 16 combinations C(4,0) + C(4,1) + C(4,2) + C(4,3) + C(4,4)

{say the cheeses are a,b,c, & d. You could have:
none ; or C(4,0) = 1 way to have no cheese
a, b, c, d ; or C(4,1) = 4 ways to have 1 cheese
ab, ac, ad, bc, bd, cd ; or C(4,2) = 6 ways to have 2 cheeses
abc, abd, acd, bcd ; or C(4,3) = 4 ways to have 3 cheeses
abcd ; or C(4,4) = 1 way to have 4 cheeses
}

The total is 6 * 32 * 16 = 3072
(Of course, 6 of these are fillingless - just bread!)
The other answers so far are assuming just one type of bread, one type of meat, & one type of cheese per sandwich only.

Answer 2

The combination of sandwich
complete sandwich
3*5*4 = 60 combination
sandwich without Cheese
3*5 = 15
sandwich without meat
3*4 =12
Another combination is sandwich without breads but what is the name (meat + cheese)
5*4 = 20

So total combination
60+15+12+20 =107

But if your defination of sandwich must have Bread
The answers is
60+15+12 =87

Answer 3

Since you can use the 3 different breads with each of the 5 different meats, you can assume that the number of combinations of bread and meat would be 5*3 or 15 different sandwhiches. Then, for each of the 15 sandwhiches we made above, we could put a different kind of cheese on (4 different kinds for each), so we can multiply the 15 above with the 4 different kinds of cheese to make 60 combinations =)

in equation form:
3 types of bread * 5 types of meat * 4 types of cheese = 60 different sandwhiches

Answer 4

3 bread* 5 meats* 4 cheese = 60 kinds of combination sandwiches for you.

Answer 5

Until you - as the sandwich shop owner - define what constitutes a "sandwich," there simply is no correct answer.

The earlier answers I saw placed too many limitations on your customers. Those Answerers lack vision, and are answering your question as mathematicians. For them, a sandwich has to have two matching slices of bread, one meat, and one cheese. In reality, this is too limiting. Some customers are vegetarians. Some customers are watching their carb intake. Some customers are lactose intolerant. 60 sandwiches does not give you enough variety to make everyone happy.

A sandwich shop will allow customers to mix/match the bread, meat, and cheese combinations beyond the 60 sandwiches you get with 3 types of bread, 5 types of meat, and 4 cheese.

I originally attempted to answer this question with a discrete number, though my logic was flawed, so I removed the erroneous portion of my answer.

Answer 6

3*5*4=60

Answer 7

60 as the other 2 answers said.. but i would also add 12 (3x4) for just cheese sandwiches for a total of 72

Answer 8

3x5x4 = 60