The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.
Choose the correct choice from the following answers
A) 220.
B) 205.
C) 250
D) 105
E) 225
different ways..   1) EASIEST approach..   lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220...   Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15..   total = 220-15= 
<gadget id="calculator">220-15</gadget>
<output>205</output>
205   ANSWER:205.
<result>B</result>
The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.