Question

There are 10 points on a line and 11 points on another line, which are parallel to each other. How many triangles can be drawn taking the vertices on any of the line?

(a) 1050

(b) 2550

(c) 150

(d) 1045

Answer 1

Correct option is (d) 1045

For a triangle, two points on one line and one on the other has to be chosen.

No. of ways = 2 points from 10 points and 1 point from 11 points or 1 point from 10 points and 2 points from 11 points = ¹⁰C₂ × ¹¹C₁ + ¹⁰C1 × ¹¹C₂

\(= \frac{10 \times 9}{2} \times 11 + 10 \times \frac{11 \times 10}{2} \)

= 495 + 550

= 1045