## LeAnn01Xxx one year ago A class has 20 students. If the teacher is randomly putting students in groups of 3 to complete a project, what is the probability that three students who are best friends will be together? 1/20 3/20 1/1,140

1. anonymous

easy way or hard way or both?

2. anonymous

actually even the hard way is not that hard

3. LeAnn01Xxx

It doesn't matter, just a way that i'll understand it.

4. anonymous

ok lets compute the number of ways to choose 3 people out of a set of 20, called "20 choose 3" and written as $$\binom{20}{3}$$ or $$_{20}C_3$$

5. anonymous

easy to do with a calculator, it is a rather large number do you know how to compute it?

6. LeAnn01Xxx

One sec. Let me get my calculator.

7. anonymous

easier to use this http://www.wolframalpha.com/input/?i=20+choose+3

8. LeAnn01Xxx

OKay so is it 3/20?

9. anonymous

oh no

10. anonymous

did you open the link i sent? $_{20}C_3=1440$

11. anonymous

that is the number of possible groups of 3 only one of them has all three best friends, so probability is $\frac{1}{1440}$

12. LeAnn01Xxx

Yeah I did.