View source for 2009 UNCO Math Contest II Problems/Problem 6

== Problem ==


Let each of <math>m</math> distinct points on the positive
<math>x</math>-axis be joined to each of <math>n</math> distinct points on
the positive <math>y</math>-axis. Assume no three segments
are concurrent (except at the axes). Obtain
with proof a formula for the number of interior
intersection points. The diagram shows that
the answer is <math>3</math> when <math>m=3</math> and <math>n=2.</math>

<asy>
draw((0,0)--(0,3),arrow=Arrow());
draw((0,0)--(4,0),arrow=Arrow());
for(int x=0;x<4;++x){
for(int y=0;y<3;++y){
D((x,0)--(0,y),black);
}}
dot(IP((2,0)--(0,1),(1,0)--(0,2)));
dot(IP((3,0)--(0,1),(1,0)--(0,2)));
dot(IP((3,0)--(0,1),(2,0)--(0,2)));
</asy>


== Solution ==
{{solution}}

== See also ==
{{UNCO Math Contest box|year=2009|n=II|num-b=5|num-a=7}}

[[Category:Introductory Combinatorics Problems]]