Two part question:
a) Show that there are n! linear orderings of {1, 2,...,n}
b) Show that n! lies between 2^{n-1} and 2^{n^2}
Is that the case, that you cannot prove this? The questions were given as a homework assignment, so I'm assuming that there is a way to prove this. It works when you do the arithmetic. For example, 2! = 2 and there are two ways to order 1 and 2: {1,2} and {2,1}. This is as far as I've gotten.