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AirRecce

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## 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.