Posted by Nichole on Wednesday, December 14, 2011 at 11:56pm.
Number of possible choices for the first point = 9.
Number of possible choices for the second point = 8.
Number of possible choices for the third point = 7.
Possible triangles with specific order of points = 9*8*7 = 504.
However, when we say triangle, we are not really concerned in which order the points are selected. So we have over-counted the number of triangles by 6, which is the number of ways to order three points.
The number of distinct triangles is therefore 504/6=84.
This number is mathematically called
9 choose 3, calculated by
9!/(3!(9-3)!) = 84
where 9! is factorial 9, = 9*8*7*...*2*1
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