ABCDE is a regular pentagon

[krishnan.anju1987]

ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A,B,C,D,E and F?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30

Hi,

I saw this question in the beatthegmat forum where the answer mentioned for this was 20. However, when I calculate using just 6C3, I do get 20. However, when I draw the images, I get 5 images as same since they are formed by joining vertices(same two pints of the pentagon). So, in my opinion the answer should be 15. It would be great if someone could clarify my doubt.

[tim]

i don't see any way that 15 can be the answer, but i will concede that there is some ambiguity in the problem. are two triangles that are congruent but have different vertices considered "different"? if so, the answer is definitely 20 because any three points of the six can be used to form a triangle (and all such sets of three points are distinct). if "different" means non-congruent, the answer is considerably less. i invite you to figure out how many distinguishable triangles there are, as that is an interesting question on its own..