Need help solving this math problem

[Pen]

"Mr. P's doctor discovered that between various doctors prescribing medicines for Mr. P, he was taking 17 different medicines in all. He was having symptoms which might be side effects of an individual drug, or any combination of 2 or more of the drugs, how many total individual plus combinations of drugs are there which might be causing Mr. P's side effect symptoms?"

 

 

Is there a formula for solving that sort of problem and if so what?

 

We started to see if we could find a pattern beginning with low numbers, like for 2 drugs, there are 3 individuals plus combos (1,2 / 1 / 2)

for 3 drugs, there are 7 individuals plus combos (1,2,3 / 1,2 / 1,3 / 2,3 / 1 / 2 / 3)

for 4 drugs, there are 15 (I think)

for 5 drugs, there are 30 (I think)

 

 

How do you go about solving such a problem?

[stripe]

I think you need to know the number of subsets of the set of 17 medicines.

http://www.mathsisfun.com/activity/subsets.html

[nmoira]

Or you could attack it as a casework counting problem.

 

One drug - 17 possibilities

two drugs - 

three drugs, etc.

 

Being careful not to over-count.  Drug 1 and Drug 2 is the same combination as Drug 2 and Drug 1.

 

What level math is this for? What unit topic is it in?

[kiana]

Don't look for the pattern with 'how many drugs are there', but instead look for the pattern as nmoira has laid out. It should end up being 2^17 - 1, but I will leave it to you to figure out how to get there. Have you had any sort of work on probability or counting recently?

 

ETA: Also, your answer for 5 is wrong. You're missing one somewhere.