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

Vedclass · Accepted Answer

$51$

Vedclass · Answer

(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

Similar Questions

How many $2$-digit numbers are there with distinct digits?

How many $3$-digit numbers are there,with no digits repeated?

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

$A$ library has $a$ copies of one book,$b$ copies of each of two books,$c$ copies of each of three books,and single copies of $d$ books. The total number of ways in which these books can be arranged is

Vedclass Test Series

Exam Paper Generator

Online Exam Module