6 points in a plane are joined in all possibl | vedclass

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(C) The number of lines formed by joining $6$ points is $^6C_2 = \frac{6 	imes 5}{2} = 15$.The total number of intersection points of these $15$ line

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$51$

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(C) The number of lines formed by joining $6$ points is $^6C_2 = \frac{6 	imes 5}{2} = 15$.The total number of intersection points of these $15$ lines,assuming no three lines are concurrent,is $^{15}C_2 = \frac{15 	imes 14}{2} = 105$.However,at each of the original $6$ points,$5$ lines intersect. Since these $5$ lines are counted as intersecting at a single point,we must subtract the extra counts.For each of the $6$ points,the number of pairs of lines intersecting at that point is $^5C_2 = 10$. Since these $10$ pairs are counted as $10$ distinct intersection points in the initial $105$,but they all represent only $1$ point,we subtract $10 - 1 = 9$ for each of the $6$ points.Total distinct points of intersection $= 105 - 6 	imes (10 - 1) = 105 - 54 = 51$.

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to:

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