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There are 12 points in a plane of which 5 are collinear. The number of triangles is
- a)200
- b)211
- c)210
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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There are 12 points in a plane of which 5 are collinear. The number of...
Explanation
- Given that there are 12 points in a plane.
- Out of these 12 points, 5 are collinear.
- To find the number of triangles that can be formed using these 12 points, we can use the combination formula.
- The number of ways to choose 3 points out of 12 is given by 12C3 = 220.
- However, we need to subtract the number of triangles that can be formed using the collinear points.
- Since 5 points are collinear, we can form triangles using these points as well.
- The number of ways to choose 3 points out of 5 collinear points is given by 5C3 = 10.
- So, the total number of triangles that can be formed using the 12 points is 220 - 10 = 210.
- Therefore, the correct answer is option C: 210.
- Given that there are 12 points in a plane.
- Out of these 12 points, 5 are collinear.
- To find the number of triangles that can be formed using these 12 points, we can use the combination formula.
- The number of ways to choose 3 points out of 12 is given by 12C3 = 220.
- However, we need to subtract the number of triangles that can be formed using the collinear points.
- Since 5 points are collinear, we can form triangles using these points as well.
- The number of ways to choose 3 points out of 5 collinear points is given by 5C3 = 10.
- So, the total number of triangles that can be formed using the 12 points is 220 - 10 = 210.
- Therefore, the correct answer is option C: 210.
Most Upvoted Answer
There are 12 points in a plane of which 5 are collinear. The number of...
Solution:
Number of ways to select 3 points out of 12 points = 12C3 = 220
Number of ways to select 3 points out of 5 collinear points = 5C3 = 10
Therefore, the number of ways to select 3 points from the 12 points that are not collinear = 220 - 10 = 210
So, the number of triangles that can be formed using these 12 points = 210
Therefore, the correct answer is option C.
Number of ways to select 3 points out of 12 points = 12C3 = 220
Number of ways to select 3 points out of 5 collinear points = 5C3 = 10
Therefore, the number of ways to select 3 points from the 12 points that are not collinear = 220 - 10 = 210
So, the number of triangles that can be formed using these 12 points = 210
Therefore, the correct answer is option C.
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There are 12 points in a plane of which 5 are collinear. The number of...
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There are 12 points in a plane of which 5 are collinear. The number of triangles isa)200b)211c)210d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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