Problem 10 : Probability (2000) - Combination Topic

( This problem is taken from Indonesian Entrance Test of State University- 2000 )


The number of triangles that can be drawn from 7 points with no three collinear points is ...
a. 30 b. 35 c. 42 d. 70 e. 210

Answer :

It's a combination case. The formula is nCr = n! / [ (n-r)!r!].
Since the triangle has 3 points so from it's problem we have :
7C3 = 7!/ [ (7-3)!.3!]
= 7.6.5.4! / 4! 3.2.1
= 7.6.5 /6
= 7.5
= 35 Answer : B