m06 Q 37

Question

There are 6 points on the plain. Any 3 points of these 6 don't lie on the same line. How many unique triangles can be drawn using these 6 points as vertices?

5
10
20
30
60

Why isn't the answer 60. We can choose 1 vertice and there are 5C2 = 10 ways to 2 choose the remain 2 vertices. 10*6 choices = 60 (10 choices each for each vertex)?

maanavrelan4gmat · Answer

Trick here is to chose 3 points at a time out of 6 available, and order does not matter.

So number of triangles = 6C3 = 10

qweert · Answer

This question tricked me too. Any how if they didn't mention "Any 3 points of these 6 don't lie on the same line" would the answer stay the same...

bblast · Answer

why not pick 2 points out of 6 ? =6C2 now since every 2 point will form a triangle with the 4 remaining points. hence answer = 6C2*4 = 60 :oops:

help me

fluke · Answer

Consider only 3 non-collinear points:

A B C
As per your formula:

Number of triangles =  C^{3}_{2}*1=3 . But, in reality it is 3/3 = 1.

Because your formula counts same triangle thrice. Thus, at the end you will have to divide by 3.

How so:

A B C are 3 points.
It will choose one line segment using two points:
AB and connect AB to C to form a triangle.
Then,
BC and connect BC to A to form a triangle.
AC and connect AC to B to form a triangle.
You see three counts for the same triangle ABC.

Divide your result by 3 and you will get the answer.

Or simply; select 3 points out of n points to know the number.

If there are n non-collinear points, where n>=3, we can make
 C^{n}_{3}  distinct triangles.

bblast · Answer

kudos fluke for polishing this up,

actually my logic is applicable when there are two parallel lines with points and we have to draw triangles among them. Math 2 has this question I guess,

This was a relatively easier question which I messed up.

m06 Q 37

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