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There are 12 points in a plane no 3 of which are collinear except that 6 points which are collinear. The number of different straight lines is ________.
- a)50
- b)51
- c)52
- d)None
Correct answer is option 'C'. Can you explain this answer?
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There are 12 points in a plane no 3 of which are collinear except that...
Given:
- 12 points in a plane
- No 3 points are collinear except for 6 points which are collinear
To find:
- The number of different straight lines
Solution:
- Total number of possible straight lines = ${12 \choose 2}$ = $\dfrac{12\times11}{2}$ = 66
- Number of straight lines passing through 6 collinear points = ${6 \choose 2}$ + 6 = 21
- Number of straight lines that can be formed using the remaining 6 points = ${6 \choose 2}$ = 15
- Total number of different straight lines = 66 - 21 + 15 = 60
However, we have overcounted the number of straight lines that pass through both the collinear points and other points.
- Number of straight lines that pass through both collinear points and other points = $6\times6$ = 36
- Number of different straight lines = 60 - 36 = 24
Therefore, the number of different straight lines is 24 + 28 = 52.
Answer: Option C - 52.
- 12 points in a plane
- No 3 points are collinear except for 6 points which are collinear
To find:
- The number of different straight lines
Solution:
- Total number of possible straight lines = ${12 \choose 2}$ = $\dfrac{12\times11}{2}$ = 66
- Number of straight lines passing through 6 collinear points = ${6 \choose 2}$ + 6 = 21
- Number of straight lines that can be formed using the remaining 6 points = ${6 \choose 2}$ = 15
- Total number of different straight lines = 66 - 21 + 15 = 60
However, we have overcounted the number of straight lines that pass through both the collinear points and other points.
- Number of straight lines that pass through both collinear points and other points = $6\times6$ = 36
- Number of different straight lines = 60 - 36 = 24
Therefore, the number of different straight lines is 24 + 28 = 52.
Answer: Option C - 52.
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Community Answer
There are 12 points in a plane no 3 of which are collinear except that...
No of line formed by joining 12 points , taking 2 at a time = 12C2 = 66
no of line formed by joining 6 points , taking 2 at a time = 6C2 = 15
But 6 collinear when joined pairwise, give only one line
so 66-15+1= 52
the correct answer is 52
no of line formed by joining 6 points , taking 2 at a time = 6C2 = 15
But 6 collinear when joined pairwise, give only one line
so 66-15+1= 52
the correct answer is 52
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There are 12 points in a plane no 3 of which are collinear except that 6 points which are collinear. The number of different straight lines is ________.a)50b)51c)52d)NoneCorrect answer is option 'C'. Can you explain this answer?
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