Rule of Sum: if a first task can be done in m ways, while a second task can be done in n ways, and the 2^nd^ task can not to be done simultaneously, then performing either task can be accomplished in any one of m+n ways. (m and n are assumed to be distinct)
Rule of Product: If a procedure can be broken down into 1^st^ and 2^nd^ stages, and there are m possible outcomes for the 1^st^ stand and n possible outcomes for the 2^nd^ stage, then we can carry out the procedure in mn ways.
Example: Casting for a movie where a couple is required. With 5 men and 6 women, how many ways can the director cast the couple.
http://www.youtube.com/watch?v=aM1fuQzWWuQ