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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$51$

Vedclass · Answer

(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:

Similar Questions

The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. $A$ total number of $m$ points are taken on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$. The maximum number of triangles formed with vertices at these points is:

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is:

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

Two squares are chosen at random on a chessboard. The probability that they have a side in common is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module