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 given by $^6C_2 = \frac{6 	imes 5}{2} = 15$ lines.The total number of intersection points for

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$51$

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(C) The number of lines formed by joining $6$ points is given by $^6C_2 = \frac{6 	imes 5}{2} = 15$ lines.The total number of intersection points formed by $15$ lines,assuming no three lines are concurrent and no two are parallel,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,but the formula $^{15}C_2$ counts all pairs of these $5$ lines as distinct intersection points,we must adjust for this.For each of the $6$ points,the number of pairs of lines passing through it is $^5C_2 = 10$. These $10$ pairs are counted as $10$ distinct points in the $105$ total,but they all represent the same original point.Thus,for each original point,we subtract $10$ and add back $1$ (the point itself). Total distinct points $= 105 - 6 	imes (10 - 1) = 105 - 6 	imes 9 = 105 - 54 = 51$.

$6$ 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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