3.4.1 Generalized Counting Rules Video
PROFESSOR: There are two generalizations of the bijection rule and the product rule that come up all the time and play an essential role in the repertoire of any counter. So let's look at those. The first of these is a generalization of the product rule. And let's see an instance where it comes up. Suppose I wanted to count the number of lineups of five students in the class. So if I let S be the number of students, and let's say, for the afternoon session S is 91, then the number of lineups of five students-- if I use the ordinary product rule, I would get-- I'm talking about S to the fifth, that is, sequences of length five of elements of S. And so the product rule would say, take 91 to the fifth as the number of lineups of five students. And that would be correct if the same student could appear twice in line, but that, of course, isn't possible with real students. So the lineups have no repeats. And what we're really counting is the number of t...