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There are 12 points in a plane of which 5 are collinear. The number of triangle is?
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There are 12 points in a plane of which 5 are collinear. The number of...
Problem:
There are 12 points in a plane of which 5 are collinear. The number of triangle is?
Solution:
Step 1: Count the total number of triangles
The total number of triangles can be calculated using the formula nC3, where n is the total number of points.
nC3 = (12C3)
= (12 x 11 x 10)/(3 x 2 x 1)
= 220
Therefore, there are 220 triangles that can be formed using the 12 points.
Step 2: Count the number of triangles that include the collinear points
Since 5 points are collinear, any triangle that includes all 5 of these points will not be counted.
There are 5C3 = 10 triangles that can be formed using these 5 points.
Therefore, the total number of triangles that include the collinear points is 10.
Step 3: Subtract the number of triangles that include the collinear points from the total number of triangles
The number of triangles that do not include the collinear points can be found by subtracting the number of triangles that include the collinear points from the total number of triangles.
Therefore, the number of triangles that do not include the collinear points is:
220 - 10 = 210.
Final Answer:
The number of triangles that can be formed using the 12 points in a plane of which 5 are collinear is 210.
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There are 12 points in a plane of which 5 are collinear. The number of triangle is?
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There are 12 points in a plane of which 5 are collinear. The number of triangle is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 12 points in a plane of which 5 are collinear. The number of triangle is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 12 points in a plane of which 5 are collinear. The number of triangle is?.
There are 12 points in a plane of which 5 are collinear. The number of triangle is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 12 points in a plane of which 5 are collinear. The number of triangle is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 12 points in a plane of which 5 are collinear. The number of triangle is?.
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