There are n points in a plane of which p poin | vedclass

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(C) Total number of points is $n$. The number of ways to select $2$ points from $n$ points to form a line is $^nC_2$.Since $p$ points are collinear,th

Vedclass · Accepted Answer

$^nC_2 - ^pC_2 + 1$

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(C) Total number of points is $n$. The number of ways to select $2$ points from $n$ points to form a line is $^nC_2$.Since $p$ points are collinear,they all lie on the same line. Selecting any $2$ points from these $p$ points results in the same line,which is counted $^pC_2$ times in $^nC_2$.To correct this,we subtract all the lines formed by the $p$ collinear points $(^pC_2)$ and add back $1$ to account for the single line that passes through all $p$ points.Therefore,the total number of distinct lines is $^nC_2 - ^pC_2 + 1$.

There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

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