In the Diagnostic and statistical manual of mental disorders, fifth edition (DSM-5), one can be diagnosed with a substance use disorder, for example, cannabis use disorder, if 2 (or more) of 12 possible symptoms have been present for 12 months or more, and if those symptoms they cause a "clinically significant deterioration or distress".
Concentrating only on the "2 of 12 symptoms" aspect, how many different symptom combinations exist so that one can be diagnosed with a substance use disorder?
This question is similar to How many ways can you paint 90 different cubes? In how many ways can "ARRANGE" be organized? (closed), and some other questions, but not similar enough for me to find the answer to my question.
There is an academic article that provides answers to similar symptom combination questions:
Galatzer-Levy, Isaac R. and Richard A. Bryant. "636,120 ways to have a posttraumatic stress disorder." Perspectives on psychological science 8, no. 6 (2013): 651-662.
The authors use "a binomial equation of n choosing k with replacement", but I don't understand how to calculate an answer using the formula. (I tried several times, but I couldn't duplicate their results). Part of the formula is:
To start, I'm not sure what k It would be for the question I am asking. I thought it would be k= 2, but I'm not sure.
The full formula is found on page 655 of the article (PDF). It would take me a long It's time to find out how to represent the formula with MathJax (and I will probably still make a mistake!), so if you don't mind looking at the article for the formula, I appreciate it very much. 🙂
Thank you! ~ Mark