Permutations Practice Test 1

Question : 34 of 40

Marks: +1, -0

The sides AB, BC, CA of a triangle ABC have 3, 5 and 6 interior points respectively on them. Thenumber of triangles that can be constructed using these points as vertices is given by:

364
333
240
None of these

Validate

Solution:

Selection of 3 points from given 14 pts can be made in

^14C_3 = 364

ways.
But selection of 3 points from the points on one line cannot give any triangle.
Such selections are

^3C_3 + ^5C_3 + ^6C_3

= 1 + 10 + 20 = 31..... (2)
Hence total number of triangles that can be formed = 364 – 31 = 333.

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