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

$15$ lines are concurrent at a point $P$. $A$ line $L$ not passing through $P$ intersects all the $15$ lines and forms triangles with them. Then the number of triangles having $L$ as one of its sides is

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

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

Three parallel straight lines $L_1, L_2$ and $L_3$ lie on the same plane. Consider $5$ points on $L_1, 7$ points on $L_2$ and $9$ points on $L_3$. Then the maximum possible number of triangles formed with vertices at these points is:

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module