The straight line S1,S2,S3 are in parallel and lie in the same
plane. A total number of A points on S1, B points on S2 and C
points on S3 are used to produce triangles .What is the maximum number of
triangles formed ?

Question

mathmath333 · Answer

The straight line $S_{1} ,S_{2},S_{3}$ are in parallel and lie in the same
plane. A total number of $A$ points on $S_{1}$, $B$ points on $S_{2}$ and $C$
points on $S_{3}$ are used to produce triangles .What is the maximum number of
triangles formed ?

$a.)\ \dbinom{A+B+C}{3}-\dbinom{A}{3}-\dbinom{B}{3}-\dbinom{C}{3}+1 \
b.)\ \dbinom{A+B+C}{3} \
c.)\ \dbinom{A+B+C}{3}+1 \
d.)\ \dbinom{A+B+C}{3}-\dbinom{A}{3}-\dbinom{B}{3}-\dbinom{C}{3} \ $

parthkohli · Answer

It's D... self-explanatory.

mathmath333 · Answer

its D but how is it self explanatory

anonymous · Answer

d hope this helps

parthkohli · Answer

First, the number of triangles you can create from $n$ non-collinear points is $\binom{n}3$. But if you have $k$ points in a straight line among the $n$, then you remove all the selections of three points from $k$ points from the total number, so $\binom{n}{3}-\binom{k}{3}$ triangles.