The number of triangles that can be formed by | vedclass

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

Question

(C) Total number of points = $5 + 3 = 8$. To form a triangle,we need to select $3$ points out of $8$,which can be done in $^8C_3$ ways. However,if the

Vedclass · Accepted Answer

$^8C_3 - ^5C_3 - ^3C_3$

Vedclass · Answer

(C) Total number of points = $5 + 3 = 8$. To form a triangle,we need to select $3$ points out of $8$,which can be done in $^8C_3$ ways. However,if the $3$ selected points are collinear,they do not form a triangle. There are $5$ points on one line,so the number of ways to select $3$ collinear points from these is $^5C_3$. There are $3$ points on the other parallel line,so the number of ways to select $3$ collinear points from these is $^3C_3$. Thus,the number of triangles = $^8C_3 - ^5C_3 - ^3C_3$.

The number of triangles that can be formed by $5$ points on a line and $3$ points on a parallel line is

Similar Questions

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is

$A$ polygon has $54$ diagonals. Then,the number of its sides is

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

$A$ polygon has $54$ diagonals. The number of sides of this polygon is

The number of diagonals in a regular polygon of $100$ sides is

Vedclass Test Series

Exam Paper Generator

Online Exam Module