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If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?

Solution:

Let 0 be the number of intersection point of first line

Let 1 be the number of intersection point of 2nd line

Let (2+1) be the number of intersection point of 3rd line

Let (3+2+1) be the number of intersection point of 4th line

Let the no. of intersection point of n^{\text {th }} line =(n-1)+(n-2) \ldots . .(3)(2)(1), in which n=20

\begin{array}{l} \mathrm{S}=(\mathrm{n}-1) \times \mathrm{n} / 2 \\ =19 \times 10 \\ =190 \end{array}

i

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