## mathmath333 one year ago 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 ?

1. mathmath333

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 ? \(a.)\ \dbinom{A+B+C}{3}-\dbinom{A}{3}-\dbinom{B}{3}-\dbinom{C}{3}+1 \\ b.)\ \dbinom{A+B+C}{3} \\ c.)\ \dbinom{A+B+C}{3}+1 \\ d.)\ \dbinom{A+B+C}{3}-\dbinom{A}{3}-\dbinom{B}{3}-\dbinom{C}{3} \\ \)

2. ParthKohli

It's D... self-explanatory.

3. mathmath333

its D but how is it self explanatory

4. anonymous

d hope this helps

5. ParthKohli

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.