There are 10 points in a plane,out of which 4 | vedclass

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(B) straight line is formed by joining any two points. Therefore,the total number of lines that can be formed by joining $10$ points is $^{10}C_2$.How

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(B) straight line is formed by joining any two points. Therefore,the total number of lines that can be formed by joining $10$ points is $^{10}C_2$.However,$4$ of these points are collinear. Joining any two of these $4$ points results in the same line.The number of lines formed by $4$ collinear points is $^{4}C_2$,which counts as only $1$ line instead of $6$.Therefore,the total number of distinct lines = $^{10}C_2 - ^{4}C_2 + 1$.Calculation: $\frac{10 	imes 9}{2} - \frac{4 	imes 3}{2} + 1 = 45 - 6 + 1 = 40$.

There are $10$ points in a plane,out of which $4$ are collinear. How many straight lines can be formed by joining any two of these points?

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