SOLUTION: Q: There are 12 points in a plane of which 5 are collinear. The number of triangles is? I think we have to combine C(5,2) (out of 5 collinear, 2 points can form a side of triang

Algebra ->  Permutations -> SOLUTION: Q: There are 12 points in a plane of which 5 are collinear. The number of triangles is? I think we have to combine C(5,2) (out of 5 collinear, 2 points can form a side of triang      Log On


   

Question 192269: Q: There are 12 points in a plane of which 5 are collinear. The number of triangles is?
I think we have to combine C(5,2) (out of 5 collinear, 2 points can form a side of triangle) with the combination of the rest of the points... but i m not getting any answer out of the four options
a)200
b)211
c)210
d)none of these
Found 3 solutions by chowmeineep, bhayzone, sEahors3:
Answer by chowmeineep(4) About Me  (Show Source):
Answer by bhayzone(8) About Me  (Show Source):
You can put this solution on YOUR website!
I think the answer is D - none of the above. I get a total of 105 triangles
I'm assuming coliner means they are on the same line.
5 points on the same line (assume they form one side of the triangle). So how many distinct 2 points (as two points constitue one side) can you select from a set of 5 points. Note side AB = Side BA so this is a combination problem.
5! div 2!*3! = 10 sides -------------- A
From the Remaining 7 points, how many triangles can you make. This is same as asking you to select 3 distinct points from 7. Again a combination problem as Triangle ABC = Triangle BAC
7! div 3!*4! = 35 -------------------- B
NOT DONE YET !!!
Each side in A can combile with each of the 7 points to make a triangle. Thus, 10 sides can make 70 triangles ----- C
Answer = C+B = 105

Answer by sEahors3(6) About Me  (Show Source):
You can put this solution on YOUR website!
(12 nCr 3) - (5 nCr 3) = 210
so it is C
medur =)