How many triangles can be obtained by joining 12 points, five of which are collinear?

Asked by Aaryan | 1 year ago |  114

##### Solution :-

We know that 3 points are required to draw a triangle and the collinear points will lie on the same line.

Number of triangles formed = (total no. of triangles formed by all 12 points) – (no. of triangles formed by collinear points)

12C3 – 5C3

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

= (2×11×10) – (5×2)

= 220 – 10

= 210

The total no. of triangles formed are 210.

Answered by Sakshi | 1 year ago

### Related Questions

#### How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

#### Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

#### How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’,

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?