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Permutations and Combination — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsPermutations and Combination1 Mark
Question
There are $20$ straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
✓

Answer

There are 20 lines such that no two of them are parallel and no three of them are concurrent. Since no two lines are parallel, they intersect at a point. ∴ Number of points of intersection if no two lines are parallel and no three lines areconcurrent $={ }^{20} C _2$
$=\frac{20 !}{2 ! 18 !}$
$=\frac{20 \times 19 \times 18 !}{2 \times 1 \times 18 !}$
$=190$

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