This stack was designed to illustrate the principal of combinations. You might think of a situation where there is a party and just before everyone leaves they all shake hands. Well just how many hand shakes is that? Remember that one does not shake his own hand (at least not at parties) and two people only shake hands once.
Thinking about this goes far beyond parties. This problem might represent the number of times different offices might contact each other in the course of a day or how many navigation routes there are between different ports at sea.
If you are interested in this sort of thing then you might try reading about Combinations and Pascale's triangle as found in any Algebra II text book. Or you could visit a library or bug a teacher or a big brother who thinks he knows it all.