Lines through pairs of five points with no three collinear

[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.

C_5,2= (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]

Welcome to PF!

Hi mathstudent88! Welcome to PF!

(hmm … 60 is a very large number … )

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.

C_5,2= (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!

but … C_5,2 = 5!/2!(5-2)! = … ?

 

[mathstudent88]

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

the answer is 10.


Thanks again!