Q. 144.5( 4 Votes )

# There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Answer :

Given that we need to find the no. of different straight lines that can be drawn from the 10 points in which 4 are collinear.

We know that 2 points are required to draw a line and the collinear points will lie on the same line, and only one line can be drawn by joining any two points of these collinear points.

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

⇒ N = (total no. of lines formed by all 10 points) – (no. of lines formed by collinear points) + 1

Here 1 is added because only 1 line can be formed by the four collinear points.

⇒ N = ^{10}C_{2} – ^{4}C_{2} + 1

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N = 45 – 6 + 1

⇒ N = 40

∴ The total no. of ways of different lines formed are 40.

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