Out of 20 points,no three points are collinea | vedclass

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(D) To form a line,we need $2$ points. The total number of ways to select $2$ points from $20$ is given by $\binom{20}{2}$.Since $4$ points are collin

Vedclass · Accepted Answer

$185$

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(D) To form a line,we need $2$ points. The total number of ways to select $2$ points from $20$ is given by $\binom{20}{2}$.Since $4$ points are collinear,the number of lines formed by these $4$ points is only $1$ instead of $\binom{4}{2}$.The formula for the number of lines is $\binom{n}{2} - \binom{m}{2} + 1$,where $n$ is the total number of points and $m$ is the number of collinear points.Here,$n = 20$ and $m = 4$.Number of lines $= \binom{20}{2} - \binom{4}{2} + 1$$= \frac{20 	imes 19}{2} - \frac{4 	imes 3}{2} + 1$$= 190 - 6 + 1 = 185$.

Out of $20$ points,no three points are collinear except for $4$ points which are collinear. How many lines can be drawn by joining these points?

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