Planar triangles
Probability
Level
1
How many distinct triangles can be formed from 10 points on a plane, no 3 of which are co-linear?
The answer is 120.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Each triangle can be formed from 3 of the 10 points. This corresponds to combinations of 3 objects out of 10. Thus, the number of triangles that can be formed is:
( 3 1 0 ) = 1 2 0 .
The assumption that "no 3 of the points are co-linear" is important for this problem. Without this assumption, a combination of 3 points would not make a triangle if those points were on the same line.