Just like when we add, the parameters are called "addends", and how division has a "dividend", "divisor", "quotient", and "remainder", what is the conventional name for the n and r in combinatorics functions nCr and nPr?
Not looking for a definition (eg, the number of items chosen as a subset from all the choices). Looking for the precise term.
Intuitively I might call the r a "selector", but I have no idea if that's the right term.
On
These are called indices of the symbol for the combinatorial quantity. Binomial coefficients are usually written using the notation $\binom nk$, in which one can refer to $n$ as the upper index and $k$ as the lower index. If a number like a Stirling number is written like $s(n,k)$ one could call them first and second indices. As for notations in which numbers are written around a central letter in all kinds of directions like the planets of Jupiter, just say no.
In section 5.1 Basic Identities in Concrete Mathematics by R.L. Graham, D.E. Knuth and O. Patashnik the authors introduce binomial coefficients and designate $n$ and $r$
\begin{align*} \binom{n}{r}={}_{n}C_{r} \end{align*} upper index and lower index.