Help with a question about collinear points

[mathstudent88]

Let P1, P2, ..., P5 be five points, no three of which are collinear. How many lines contain two of these five points?


How I thought about solving this was by way of combinations.

C5,2= (5*4*3*2)/2 = 60.


So there would be 60 lines that contain 2 of the 5 points. Is this a good way to approach this problem or is there a better way?

Thank you for your help!

[tiny-tim]

Hi mathstudent88! Welcome to PF! :smile:

(hmm … 60 is a very large number … :rolleyes:)
Let P1, P2, ..., P5 be five points, no three of which are collinear. How many lines contain two of these five points?

How I thought about solving this was by way of combinations.

C5,2= (5*4*3*2)/2 = 60.

So there would be 60 lines that contain 2 of the 5 points. Is this a good way to approach this problem or is there a better way?

No … combinations is exactly the right way! :smile:

but … C5,2 = 5!/2!(5-2)! = … ? :wink:

[mathstudent88]

haha I forgot all about the (5-2)! part... thank you for pointing it out for me!!

the answer is 10.


Thanks again!!