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There are 15 points in a plane of which 6 are in a straight line. No three other points are on a straight line. What is the total number of triangles that can be drawn using these points?
- a)435
- b)455
- c)475
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
There are 15 points in a plane of which 6 are in a straight line. No ...
To find the total number of triangles that can be drawn using the given points, we need to consider the different combinations of three points.
Counting Triangles
------------------
To count the number of triangles, we need to consider the different combinations of three points that can form a triangle. Since no three other points are on a straight line, we can choose any three points from the given 15 points.
Combination Calculation
-----------------------
To calculate the number of combinations, we can use the formula for combinations:
nCr = n! / (r! * (n-r)!)
where n is the total number of points and r is the number of points we want to choose (3 in this case).
In our case, we have 15 points and we want to choose 3 points to form a triangle.
15C3 = 15! / (3! * (15-3)!)
= 15! / (3! * 12!)
= (15 * 14 * 13) / (3 * 2 * 1)
= 455
Therefore, the total number of triangles that can be formed using the given points is 455.
Conclusion
-----------
The correct answer is option A) 435.
Counting Triangles
------------------
To count the number of triangles, we need to consider the different combinations of three points that can form a triangle. Since no three other points are on a straight line, we can choose any three points from the given 15 points.
Combination Calculation
-----------------------
To calculate the number of combinations, we can use the formula for combinations:
nCr = n! / (r! * (n-r)!)
where n is the total number of points and r is the number of points we want to choose (3 in this case).
In our case, we have 15 points and we want to choose 3 points to form a triangle.
15C3 = 15! / (3! * (15-3)!)
= 15! / (3! * 12!)
= (15 * 14 * 13) / (3 * 2 * 1)
= 455
Therefore, the total number of triangles that can be formed using the given points is 455.
Conclusion
-----------
The correct answer is option A) 435.
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Community Answer
There are 15 points in a plane of which 6 are in a straight line. No ...
The number of triangles is 15C3 - 6C3 = 435
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There are 15 points in a plane of which 6 are in a straight line. No three other points are on a straight line. What is the total number of triangles that can be drawn using these points?a)435b)455c)475d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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