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There are 16 points in a plane in which 6 are collinear. How many lines can be drawn by joining these points?
- a)106
- b)105
- c)60
- d)55
Correct answer is option 'A'. Can you explain this answer?
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There are 16 points in a plane in which 6 are collinear. How many line...
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There are 16 points in a plane in which 6 are collinear. How many line...
Solution:
Given, there are 16 points in a plane in which 6 are collinear.
Number of lines that can be formed by joining 16 points is = (16C2) = 120
But, out of these 120 lines, 6 lines are straight lines which are formed by joining collinear points.
So, the number of lines that can be drawn by joining these points = 120 - 6 = 114
But, we have to exclude the lines that have no more than 2 points on them.
Number of lines that can be formed by joining 2 points = (16C2 - 16) = 104
So, the required number of lines = 114 - 104 = 10 + 96 = 106.
Hence, the correct answer is option 'A', 106.
Given, there are 16 points in a plane in which 6 are collinear.
Number of lines that can be formed by joining 16 points is = (16C2) = 120
But, out of these 120 lines, 6 lines are straight lines which are formed by joining collinear points.
So, the number of lines that can be drawn by joining these points = 120 - 6 = 114
But, we have to exclude the lines that have no more than 2 points on them.
Number of lines that can be formed by joining 2 points = (16C2 - 16) = 104
So, the required number of lines = 114 - 104 = 10 + 96 = 106.
Hence, the correct answer is option 'A', 106.
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There are 16 points in a plane in which 6 are collinear. How many lines can be drawn by joining these points?a)106b)105c)60d)55Correct answer is option 'A'. Can you explain this answer?
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