# Math Help - Functions and Combinatorics?

1. ## Functions and Combinatorics?

Let $S = \{1,2,3,\mbox{...}, 10\}$. If $m$ is the number of ways of selecting $p$ and $q$ from the set $S$ such that the function $f(x) = \frac{x^3}{3} + \frac{p}{2}x^2 + qx + 10$ is a one-one function and $n$ is the number of ways of selecting $p$ and $q$ from the set $S$ such that $|p - q| < 4$, determine the greater of the two numbers.

Spoiler:
$m = 62,\ n = 52$

How to do it?

2. 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.