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

Question

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

anonymous · Answer

easy way or hard way or both?

anonymous · Answer

actually even the hard way is not that hard

leann01xxx · Answer

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

anonymous · Answer

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 $_{20}C_3$

anonymous · Answer

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

leann01xxx · Answer

One sec. Let me get my calculator.

anonymous · Answer

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

leann01xxx · Answer

OKay so is it 3/20?

anonymous · Answer

oh no

anonymous · Answer

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

anonymous · Answer

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

leann01xxx · Answer

Yeah I did.