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The number of triangles that can be form...

The number of triangles that can be formed by choosing from a set of 12 points, seven of which lie on the same straight line, are:

A

105

B

15

C

175

D

185

Text Solution

Verified by Experts

The correct Answer is:
D
Total number of triangles formed from 12 points taking 3 at a time `= ""^(12)C_(3)`
But out of 12 points 7 are collinear. So, these 7 points constitute a straight line mean no triangle is formed by joining these 7 points.
`therefore` Required number of triangles `= ""^(12)C_(3) - ""^(7)C_(3) = 220 - 35 = 185`
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