General formula for a combination of four categories

[AirRecce]

Homework Statement

Say I have four categories which make up a "whole" that I'll call a unique "deal".

Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or positive integers). How do I write a general expression to find out the possible number of unique "deals"?

Homework Equations

For a combination with a set number of items selected from a set whole, we would use the formula:

(n!) / (r!(n-r)!) , where r = number of objects pulled from a set of n objects

But in this case, we want any combination of the above, not just a set number of r objects. So I think the answer depends on a summation of all the possible values of r from 1-n for the set of n objects

The Attempt at a Solution

set = I + J + K + L = n
objects = r

so Σ = [ ((n!) / (1!(n-1)!)) + ((n!) / (2!(n-2)!)) ... ((n!)/(n!(n-n)!) ]
r=1

But this is including cases where there are no investors or properties in some of the combinations, which I don't want.

 

[CWatters]

If I understand you correctly I think you just multiply the number of each valid option. For example if "I" can take one of 9 values, "J" can take one of 5 values and ,"L" one of 4 values the number of combinations is

9 * 5 * 4 ...

 

[CWatters]

PS You have a problem if some values can be any positive integer because there are an infinite number of positive integers.

 

[tnich]

Homework Statement

Say I have four categories which make up a "whole" that I'll call a unique "deal".

Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or positive integers). How do I write a general expression to find out the possible number of unique "deals"?

I think part of your confusion stems from not having a complete statement of the problem. Is J the total number of possible investors, so that the number of investors in a given deal is j∈{1, 2, . . . J}?
Is a sum the right way to determine combinations? If you have for example, 2 possible combinations of properties, 3 possible combinations of investors, 1 possible combination of credit lines, 1 possible combination of mortgages, how many possible combinations of properties, investors, credit lines and mortgages would you have?