Q. 165.0( 1 Vote )

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

Answer :

Given that we need to find the no. of triangles that can be drawn from the 12 points in which 5 are collinear.

We know that 3 points are required to draw a triangle and the collinear points will lie on the same line, and no triangle can be drawn by joining any three points of these collinear points.

Let us assume the no. of triangles formed be N,

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

⇒ N = ^{12}C_{3} – ^{5}C_{3}

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N = 220 – 10

⇒ N = 210

∴ The total no. of triangles formed are 210.

Rate this question :

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

RD Sharma - MathematicsA committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of :

at least 3 girls?

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

4 letters are used at a time

RD Sharma - MathematicsA parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.

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

all letters are used at a time

RD Sharma - MathematicsOut of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines (ii) triangles can be formed by joining them?

RD Sharma - Mathematics