Triangles Formed by Diameters and Center
CAT 2017 Slot 1 · Quantitative Ability · Hard · Permutation and Combination
This is a hard Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Permutation and Combination. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.
Let and be five diameters of a circle with center at . In how many ways can three points be chosen out of and so as to form a triangle?
160
Explanation
Total points = 11 (10 on circle, 1 center ). Total choices of 3 points = . Collinear triplets cannot form a triangle. Collinear triplets are formed only by the 2 endpoints of a diameter and the center . There are 5 diameters, so 5 sets of collinear triplets: Number of triangles = .
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