The title of this section, “Counting,” is not intended to evoke the usual process of counting sheep, or counting change. What we want is to be able to count some collection in principle so that we wil...The title of this section, “Counting,” is not intended to evoke the usual process of counting sheep, or counting change. What we want is to be able to count some collection in principle so that we will be able to discover a formula for its size. There are two principles that will be indispensable in counting things: the “multiplication rule” which tells us when we should multiply, and the “addition rule” which tells us when we should add.
In working examples from the previous two sections you may have noticed that we often need to count the number of non-repetitive lists of length n that are made from n symbols. This kind of problem oc...In working examples from the previous two sections you may have noticed that we often need to count the number of non-repetitive lists of length n that are made from n symbols. This kind of problem occurs so often that a special idea, called a factorial, is used to handle it.
