Pronunciation of Permutation/Combination Notation and Ordered Pairs

Question

Quick question: How am I supposed to pronounce (or read in my head) the following?

$P(n,k)$ or $C(n,k)$

Also, how am I supposed to pronounce (or read in my head) this?

$K \times M = \{(x,y): x\in K$ and $y\in M\}$

Answer 1

I would pronounce the first two "permute $n$ $k$" and "choose $n$ $k$". But the equivalent $\binom{n}{k}$ I would pronounce "$n$ choose $k$", which I think is a better name for the concept, so pronouncing it that way makes sense too.

In the second question, not sure if you're asking how to pronounce just $K \times R$ or the whole equation.

I'd pronounce the left side "$K$ cross $R$" and I would pronounce the whole equation "$K$ cross $R$ equals the set of all $x$, $y$ such that $x$ is in $K$ and $y$ is in $R$", but there are a million different ways.

Answer 2

$P(n,k)$ is pronounced the number of $k$ such permutations of $n$ and $C(n,k)$ is pronounced $n$ choose $k$.