# What is the proper term for the "n" and "r" in the combination/permutation (nCr, nPr) functions?

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.

• I'm not aware of any. Feb 1 at 20:49
• nice one ! let's take something simpler, $1 + x + x^2+...+ x^k+...+x^n$, then n is called degree. What's the name of k ? Feb 1 at 21:38
• @Boyku exponent or power? Feb 1 at 21:43
• Choosing is subtraction. Given the combinatorial context, the subtraction becomes much much more dificult combinatorics.fandom.com/wiki/Subtraction_Tables : minuend and subtrahend. Feb 1 at 21:55

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.
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.
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