There are 10 points in a plane of which no th | vedclass

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

Question

(B) Total points = $10$. Points that are collinear = $4$. Points that are non-collinear = $6$. To form a triangle with at least one vertex from the $4

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(B) Total points = $10$. Points that are collinear = $4$. Points that are non-collinear = $6$. To form a triangle with at least one vertex from the $4$ collinear points,we consider two cases: Case $1$: One vertex from the $4$ collinear points and two vertices from the $6$ non-collinear points. Number of triangles = $^4C_1 	imes ^6C_2 = 4 	imes 15 = 60$. Case $2$: Two vertices from the $4$ collinear points and one vertex from the $6$ non-collinear points. Number of triangles = $^4C_2 	imes ^6C_1 = 6 	imes 6 = 36$. Total number of triangles = $60 + 36 = 96$.

There are $10$ points in a plane of which no three points are collinear except $4$ points. The number of distinct triangles that can be formed by joining these points such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is:

Similar Questions

If in a regular polygon the number of diagonals is $54$,then the number of sides of this polygon is

There are $10$ points on the line segment $AB$ excluding $A$ and $B$,and $8$ points on the line segment $AC$ excluding $A$ and $C$. The number of triangles formed using these $18$ points (excluding $A, B,$ and $C$) is:

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points blue and the rest red. If the number of red and blue line segments are equal,then the value of $n$ 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:

$T_m$ denotes the number of triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$,then $m$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module