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There are 15 points in a plane, out of which 6 are collinear. How many pentagons can be drawn with these points?
- a)3006
- b)3003
- c)2997
- d)3004
- e)3009
Correct answer is option 'C'. Can you explain this answer?
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There are 15 points in a plane, out of which 6 are collinear. How many...
Solution:
To form a pentagon, we need to choose 5 points out of 15 points.
Total number of ways to choose 5 points out of 15 points = 15C5 = 3003
But out of these 3003 pentagons, some pentagons can be formed using the 6 collinear points.
Number of ways to choose 5 points out of 6 collinear points = 6C5 = 6
Number of pentagons that can be formed using the 6 collinear points = 6
Therefore, the total number of pentagons that can be formed using the given 15 points = 3003 - 6 = 2997
Hence, the correct option is (c) 2997.
To form a pentagon, we need to choose 5 points out of 15 points.
Total number of ways to choose 5 points out of 15 points = 15C5 = 3003
But out of these 3003 pentagons, some pentagons can be formed using the 6 collinear points.
Number of ways to choose 5 points out of 6 collinear points = 6C5 = 6
Number of pentagons that can be formed using the 6 collinear points = 6
Therefore, the total number of pentagons that can be formed using the given 15 points = 3003 - 6 = 2997
Hence, the correct option is (c) 2997.
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There are 15 points in a plane, out of which 6 are collinear. How many pentagons can be drawn with these points?a)3006b)3003c)2997d)3004e)3009Correct answer is option 'C'. Can you explain this answer?
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