Question

If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total no of points of intersection are 

a. 45

b. 40

c. 101

d. 210​

Answer 1

Answer is "A.45"

I hope it's help you.

Answer 2

A) 45

Given:

(i) No 2 lines are parallel.

$\iff$ All lines are Non-Parallel and Intersecting.

(ii) No 3 lines are concurrent.

$\implies$ 2 lines may be concurrent.

Solution:

As, one point of intersection is created by the combination of any two straight lines.

Therefore, the number of points of intersection made by 10 straight lines

$= \dbinom{10}{2} = \: ^{10}C_{2} = \dfrac{10!}{2!(10 - 2)!}$

$= \dfrac{10 \times 9 \times \cancel{8!}}{2! \times \cancel{8!}} = \dfrac{10 \times 9}{2}$

$= \boxed{45}$