JEE Exam  >  JEE Questions  >  Number of triangles formed by joining 12 poin... Start Learning for Free
Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, is
  • a)
    185
  • b)
    220
  • c)
    792
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Number of triangles formed by joining 12 points, no three of which are...
Solution:

Given,
- 12 points
- 7 of them are in a straight line

We need to find the number of triangles formed by joining these points.

To find the solution, we can use the following approach:

Step 1: Find the number of triangles formed by selecting any 3 points out of 12 points.
- This can be done by using the formula nC3, where n is the total number of points.
- nC3 = 12C3 = (12 * 11 * 10) / (3 * 2 * 1) = 220

Step 2: Find the number of triangles that contain the 7 points in a straight line.
- To form a triangle with these 7 points, we need to select 2 points from the remaining 5 points.
- The number of ways to select 2 points from 5 points is 5C2 = (5 * 4) / (2 * 1) = 10
- Since there are 7 points in a straight line, we can form 7 * 10 = 70 triangles with these points.

Step 3: Subtract the number of triangles formed with the 7 points in a straight line from the total number of triangles formed.
- Number of triangles formed = 220 - 70 = 150

Step 4: Find the number of triangles that can be formed by the remaining points.
- To find this, we need to subtract the number of triangles formed with the 7 points in a straight line from the total number of triangles that can be formed with all 12 points.
- Total number of triangles that can be formed with all 12 points = 220
- Number of triangles formed with the 7 points in a straight line = 70
- Number of triangles that can be formed with the remaining points = 220 - 70 = 150

Step 5: Add the number of triangles formed with the 7 points in a straight line to the number of triangles that can be formed with the remaining points.
- Number of triangles formed with the 7 points in a straight line = 70
- Number of triangles that can be formed with the remaining points = 150
- Total number of triangles formed = 70 + 150 = 220

Therefore, the correct answer is option A) 185.
Explore Courses for JEE exam
Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Number of triangles formed by joining 12 points, no three of which are in the same straight line except 7 of them which are in a straight line, isa)185b)220c)792d)none of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev