There are 10 points in a plane and 4 of them are collinear. The number

1.	There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is :A. 45 B. 40 C. 39 D. 38
Answer» Option : (B) Number of straight lines formed by joining the 10 points if we take 2 points at a time = ¹⁰C₂ = \(\frac{10}{2}\times \frac{9}{1}\) = 45 Number of straight lines formed by joining the 4 points if we take 2 points at a time = ⁴C₂ = \(\frac{4}{2}\times \frac{3}{1}\) = 6 But, 4 collinear points, when joined in pairs give only one line. ∴ Required number of straight lines = 45 – 6 + 1 = 40

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is :A. 45 B. 40 C. 39 D. 38

Answer»

Option : (B)

Number of straight lines formed by joining the 10 points if we take 2 points at a time = ¹⁰C₂

= \(\frac{10}{2}\times \frac{9}{1}\)

= 45

Number of straight lines formed by joining the 4 points if we take 2 points at a time = ⁴C₂

= \(\frac{4}{2}\times \frac{3}{1}\)

= 6

But,

4 collinear points, when joined in pairs give only one line.

∴ Required number of straight lines = 45 – 6 + 1

= 40