Question

There are 25 points on a plane of which 7 are collinear .
How many quadrilaterals can be formed from these points ?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ There are 25 points on a plane of which 7 are collinear . }\hspace{.33em}\\~\\
& \normalsize \text{ How many quadrilaterals can be formed from these points ?}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

So there are two groups of points, 7 collinear, and 18 non-colinnear.

Answer 3

yes

Answer 4

And there cannot be 3 or more points in a quad which are collinear.

Answer 5

See if you can think along those lines.
I'll be back.

Answer 6

18C4

Answer 7

Let A,B,C,D,E,F,G be the 7 collinear points. Let H through Y be the other non-collinear points.


Maybe break it up into cases


Case 1: All four points are chosen from the set `{H, I, J, ..., X, Y}`


Case 2: Three points are chosen from the set `{H, I, J, ..., X, Y}` while one point is chosen from `{A,B,C,D,E,F,G}`


Case 3: Two points are chosen from the set `{H, I, J, ..., X, Y}` and two points are chosen from `{A,B,C,D,E,F,G}`


It's impossible to have 1 point chosen from the set `{H, I, J, ..., X, Y}` and have 3 points chosen from `{A,B,C,D,E,F,G}` because you'd have a triangle forming instead of a quadrilateral. You cannot choose 4 points from `{A,B,C,D,E,F,G}` because you'd have a line only.