# There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Given that we need to find the no. of different straight lines that can be drawn from the 10 points in which 4 are collinear.

We know that 2 points are required to draw a line and the collinear points will lie on the same line, and only one line can be drawn by joining any two points of these collinear points.

Let us assume the no. of lines formed be N,

N = (total no. of lines formed by all 10 points) – (no. of lines formed by collinear points) + 1

Here 1 is added because only 1 line can be formed by the four collinear points.

N = 10C24C2 + 1

We know that ,

And also n! = (n)(n – 1)......2.1

N = 45 – 6 + 1

N = 40

The total no. of ways of different lines formed are 40.

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