Out of 18 points in a plane, no three are in the same line except five points which
are collinear. Find the number of lines that can be formed joining the point.

Question

Out of 18 points in a plane, no three are in the same line except five points which
are collinear. Find the number of lines that can be formed joining the point.

dan815 · Answer

mathslover will help u

mathslover · Answer

I will for sure :) But if he tells what he tried yet, will be awesome.

goformit100 · Answer

I did in this way  Sir is it correct ?

 Number of straight lines =18C2–5C2+ 1

goformit100 · Answer

What to do next ?

anonymous · Answer

Presume that absolutely no 3 are collinear -- how many lines could you make out of 18 points? Surely it's just the same as the number of combinations of 2 points you could make out of the total 18, i.e. $_{18}C_2=18!/(2!16!)=9\times17=153$

Now, recall that five of our points are collinear -- so any combinations of 2 points from these 5 actually yield the same line. How many ways could this be? Well, $$_5C_2=5!/(2!3!)=5\times2=10$$

So the total number of lines ignoring the line on which these 5 lie would just be the difference $153-10=143$... but we have to remember to count said line once, so we add $143+1=144$.

goformit100 · Answer

ok

dan815 · Answer

perfect explaination

mathslover · Answer

You did it correct goformit, this time, excellent! (y)

anonymous · Answer

I only submit after I saw he already did it correctly :-)