Question

Ten points are marked on a straight line and 11 points are marked on another straight line. How many triangles can be constructed with vertices from among the above points

Options

• 495

• 550

• 1045

• 2475

Answer 1

1045

Explanation:

Triangle is formed by picking 3 points 2 from 1st line and 1 from 2nd or 1 point from 1st line or 2 from 2nd i.e.

⇒ `""^10C_2 xx ""^11C_1 + ""^10C_1 + ""^11C_2`

`= (10!)/(2!8!) xx (11!)/(1!10!) + (10!)/(1!9!) xx (11!)/(2!9!)`

⇒ 45 × 11 + 10 × 55

= 495 + 550 = 1045