Number of lines (Dan Dima)

Discuss about this problem

http://math.smsu.edu/~les/POW07_04.html Given the a x b x c array of points in space whose first coordinates come from the set {1,2,...,a}, whose second coordinates come from the set {1,2,...,b} and whose third coordinates come from the set {1,2,...,c}, what is the total number of lines determined by all pairs of these points? You may try also to count the number of distinct planes determined by three points. Please send us a simpler description.