There are 25 points on a plane which 7 are collinear. now solve the following?
How many quadrilateras can be formed from these points?
a)5206
B)2603
3)13015
4) None of these
I wish to know if there can be a formula that will help me solve the question. Like for triangles N(N-1)(N-2)/6
Dear Sanchit,
We need not remember a formula to answer questions like these. Instead let us get into some logic.
Let us say there are ‘n’ points on a plane of which no three are collinear.
In order to draw a line since we need 2 points and from the given ‘n’ points we can select 2 points in ways.
Hence the total number of lines that can be drawn using these ‘n’ points is
Similarly for a triangle since we need 3 points, the total number of triangles that can be drawn will be
Now out of the given ‘n’ points if ‘m’ points are collinear,
The total number of straight lines will be (Here 1 is added because all the ‘m’ collinear points will give one line)
The total number of triangles will be
So coming to your question the answer will be .
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