Permutations and Combinations are usually taught in Statistics courses and, as well, in many Algebra courses.

First let's talk about factorial notation. If we write 6! (read six factorial) we mean 6*5*4*3*2*1 or 720. More generally, n! = n*(n-1)*(n-2)*...*3*2*1. Also it is agreed that 0! = 1. Check for yourself that 3! = 6, 9! = 362880, etc.

Combinations. C(n,r) indicates the number of combinations of n items taken r at a time. For example if you are going to pick three books out of six to read on your vacation, there are C(6,3) = 6 ways this can be done. In courses on the subject it it shown that C(n,r) = n!/(r!*(n-r)!). Of course, r should always be smaller than or equal to n.

Permutations. P(n,r) stands for the number of different permutations of n things chosen r at a time. Thus if you wish to chose three books from a group of six books, and then arrange the three books in order on a shelf, you have P(6,3) = 6!/3! = 6*5*4 = 120 ways of doing this. In courses on the subject it it shown that C(n,r) = n!/(n-r)!. Again, r should not be greater than n.

The last area lists the possible permutations of integers. Unfortunately it is a memory hog; so it only works for very small integers. Enjoy it anyway!