Latest CAT Aptitude Question SOLUTION: The local park at Raghu's house is in the shape of a triangle. There are 4 posts along the longest side of the park and 2 and 3 posts along the other two sides respectively. If non

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The local park at Raghu's house is in the shape of a triangle. There are 4 posts along the longest side of the park and 2 and 3 posts along the other two sides respectively. If none of these posts is at any of the corners of the park, find the number of triangles that are possible with vertices at these posts.

Option
(1) 84
(2) 79
(3) 72
(4) None of these

Asked In CAT (10 years ago)

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P.Someshwar Reddy  (10 years ago)

answer is option (2): 79

Given there are 4 posts on the longest side of the park and 2 and 3 posts on the other two sides.
So total number of posts are 4+3+2=9

To form a triangle we require 3 points,
so with 9 points we can form 9C3 triangles i.e. 84 triangles
but as we know one of the side has 3 points in same line and other side has 4 points on same line, which means they are collinear.
since collinear points do not form a triangle we need to eliminate those possibilities.

i.e. 9C3-(3C3+4C3)
=> 84-(1+4)
=>84-5
=>79

so answer is option (2): 79

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