Question

In how many ways can a committee be chosen from among 15 people if you must have at least 3 people on the committee?

Answer 1

This is 15 choose 3, since the committee positions are indistinguishable.

Answer 2

Wait, you also want to add up 15 choose 4 as well...

Answer 3

So you want to sum over 15 choose n where n = 3 to 15

Answer 4

@M0j0jojo Does this make sense to you?

Answer 5

Please say something.

Answer 6

the answer is 32887

Answer 7

but like i dont know how to get it

Answer 8

I think what you have to do is 15C3 + 15C4 +15C5...up to 15C15. but i still dont get the right answer

Answer 9

wio your answer is right but i dont get it

Answer 10

The answer should be 32887

Answer 11

lol is this question really that hard that moderators are leaving too

Answer 12

Sorry, I had to do something.

Answer 13

There are two ways to approach this problem.
You can sum up 15C3 + 15C4 + ... + 15C15
Or you can sum up 15C0 + 15C1 + 15C2 and subtract if from 15C0 + 15C1 + ... + 15C15

Answer 14

subtract if from

Answer 15

Essentially, this is the method of counting the opposite event and then subtracting it from the entire number events.

Answer 16

okay thanks

Answer 17

I used a short cut to do 15C0 + ... + 15C15.

This is basically asking how many ways are there to form a committee period. We know that every person is either in the committee or not in the committee, so we have 2^15.

Another way to do this, which is more mathematical, is to use the binomial theorem.
I'll attack below what I mean.

Answer 18

Sorry if it looked like I was stuck, I just wasn't actually around to answer your question.

Answer 19

Doesn't look like 32887 http://www.wolframalpha.com/input/?i=Sum+from+n%3D3+to+n%3D15+of+15+choose+n