Let ABC be a triangle. Consider four points 
on the side AB , five points 
on the side 
, and four points 
on the side AC . None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points 
, is 
.
Text Solution
Verified by Experts660
(660)
Points: 4 on 
on 
on AC. For a valid pentagon, no 3 vertices can be collinear, so at most 2 points from each side.
Only valid distribution 
with 
and each 
is permutations of 
:
Total 
.
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