1. The problem statement, all variables and given/known data To make sure I don't get booted right off the bat, I should emphasize that this is not a homework assignment. I'm a lawyer working on a brief, and I'm trying to respond to an allegation that has dragged combinatorics into the case. In a complaint filed in court, you are not permitted to make formulaic allegations that don't include sufficient factual allegations to properly state a claim. My problem is that a plaintiff has filed a complaint against my client (and 70+ other defendants) alleging generally that each of the 70+ defendants worked with one or more of nine different toxic substances and that they then performed one or more of eleven different activities with one or more of the nine different toxic substances. I've already referred to this as the PowerBall Approach in my brief, and a friend with a math background was able to tell me that it falls into the realm of combinatorics. But beyond that, I'm simply out of my element. I've already argued that if each defendant worked with only one substance and did only one activity, it would still describe 99 possible claims against each defendant, but that's as far as my math background can take me. 2. Relevant equations No idea, though if my situation were simpler it would apparently be (n+m-1)!/(n-1)!*m! but it's not that simple. 3. The attempt at a solution I tried finding an online combinatorics calculator (I was surprised they actually exist), but I think this is another level of complexity beyond that. For instance, those calculators could tell me how many ways you can get 2 substances out of nine substances (45), but it doesn't have to be 2 substances. It can be anywhere from 1 to nine. And then, it can be any one or more of eleven different activities with all of those possible combinations of substances. I want to give the judge a number and an equation to show where the number comes from to make clear how vague and all encompassing that count of the complaint actually is. Thanks (sorry I couldn't make a better attempt at the math but this is definitely not what they taught us in law school).