Question

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

Answer 1

Given as

The total number of points = 10

The number of collinear points = 4

The number of lines formed = (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.

= ¹⁰C₂ – ⁴C₂ + 1

On using the formula,

ⁿC_r = n!/r!(n – r)!

= 90/2 – 12/2 + 1

= 45 – 6 + 1

= 40

Hence, the total no. of ways of different lines formed are 40.