# List of Combinations

• October 10th 2011, 08:16 PM
Will57
List of Combinations
A generic combination = {A,B,C,D,E}, where each capital letter takes on one of the values from its set.

A = {a1,a2,a3}
B = {b1,b2}
C = {c1,c2,c3}
D = {d1,d2,d3}
E = {e1,e2,e3,e4}

An example of a possible combination would be combination(x) = {a1,b2,c2,d1,e4}.

How many combinations are there? How can I generate a list with all of the combinations? Or, best, can you generate the list and attach it?

I took my real-world problem and abstracted it to its fundamentals hoping that it would make it possible for one of you to solve the underlying logic.

Any help very much appreciated. I didn't take any courses in this type of math and unfortunately I don't have anyone I can run this by for help. Thanks!
• October 10th 2011, 10:46 PM
Will57
Re: List of Combinations
Quote:

Originally Posted by Will57
How many combinations are there?

On this question, I was thinking that I may be able to figure the number of combinations one stage at a time like this (((((E & D) & C)& B) &A)?

Something like what is explained here: Combination -- from Wolfram MathWorld

What I really need is the full list of combinations, and I'll be happy to clarify if asked.
• October 11th 2011, 03:47 AM
Plato
Re: List of Combinations
Quote:

Originally Posted by Will57
A generic combination = {A,B,C,D,E}, where each capital letter takes on one of the values from its set.
A = {a1,a2,a3}
B = {b1,b2}
C = {c1,c2,c3}
D = {d1,d2,d3}
E = {e1,e2,e3,e4}
An example of a possible combination would be combination(x) = {a1,b2,c2,d1,e4}. How many combinations are there?

The difficulty with such a problem is in its meaning.
As I read it, we take one from each set.
In this example there are $3\cdot 2\cdot 3\cdot 3\cdot 4=216$ possible selections.

Do you see how to count the selections?
• October 11th 2011, 09:26 AM
Will57
Re: List of Combinations
Great! That was my first thought but I was second guessing myself. You've interpreted it correctly, it's just the total number of possible combinations.

I should be able to build out the 216 in Excel in about 15 mins.

How could I go about generating a list of the combinations the next time that this comes up when there are more results (i.e. >20,000 combinations)?

I'm thinking of dusting off Mathematica to see if there is a function that will do that for me, since that program doesn't object to large calculations (even if it can lock up the computer for a few minutes).

It's always nice when the problem turns out to be easier than I had imagined! Thanks for the help, William.