How many triangles can be formed using 5 poin | 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 that are not collinear. The total number of ways to select $

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 that are not collinear. The total number of ways to select $3$ points from $8$ is $^8C_3$. However,selecting $3$ points from the $5$ collinear points on the first line does not form a triangle. Similarly,selecting $3$ points from the $3$ collinear points on the second line does not form a triangle. Therefore,the number of triangles = $^8C_3 - ^5C_3 - ^3C_3$. Calculating the values: $^8C_3 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$,$^5C_3 = \frac{5 	imes 4}{2 	imes 1} = 10$,and $^3C_3 = 1$. Number of triangles = $56 - 10 - 1 = 45$.

How many triangles can be formed using $5$ points on a line and $3$ points on a parallel line?

Similar Questions

On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices is:

If three vertices are chosen from the six vertices of a regular hexagon and joined to form a triangle,what is the probability that the triangle formed is an equilateral triangle?

$A$ set of $10$ parallel lines is intersected by another set of $m$ parallel lines. If the total number of parallelograms formed by these two sets of lines is $675$,then $m$ is equal to:

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$-sided regular polygon is

How many chords can be drawn through $21$ points on a circle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module