Care to try your hand at this elementary math problem?

Nothing required beyond what you learned in elementary school.

13 people set up 3 committees of 9 people each. There is obviously going to be some overlap. What is the minimum number of people who are members of all 3 committees?

After I thought of this problem and found the answer, the solution process was not very satisfactory because it could not be easily generalized.

I posted the problem on Math Stack Exchange and somebody gave a very simple method for taking a group of any size and finding the minimum number of people belonging to all of any number of committees of varying sizes. I am curious to see if anybody comes up with that method.