Thread: Functions and Combinatorics?

Let . If is the number of ways of selecting and from the set such that the function is a one-one function and is the number of ways of selecting and from the set such that , determine the greater of the two numbers.

Answer:

Spoiler:

How to do it?

A function is one-to-one if and only if it is either strictly increasing or strictly decreasing.

So take the derivative and see if you can work from there.