There are 10 points on the line segment AB ex | vedclass

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

Question

(C) Total points available excluding $A, B,$ and $C$ are $10 + 8 = 18$. To form a triangle,we need to select $3$ points that are not collinear. The to

Vedclass · Accepted Answer

$640$

Vedclass · Answer

(C) Total points available excluding $A, B,$ and $C$ are $10 + 8 = 18$. To form a triangle,we need to select $3$ points that are not collinear. The total number of ways to select $3$ points from $18$ is $^{18}C_3$. Points on line $AB$ are collinear,so $^{10}C_3$ combinations do not form a triangle. Points on line $AC$ are collinear,so $^{8}C_3$ combinations do not form a triangle. Thus,the number of triangles is $^{18}C_3 - ^{10}C_3 - ^{8}C_3$. $^{18}C_3 = \frac{18 	imes 17 	imes 16}{3 	imes 2 	imes 1} = 816$. $^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$. $^{8}C_3 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$. Number of triangles $= 816 - 120 - 56 = 640$.

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:

Similar Questions

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?

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

$15$ persons are sitting around a circular table. The number of ways of selecting three persons at a time from them,such that the selected three do not sit together at one place is

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module