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A quite unimportant, but still systematically necessary question is how you go about pronouncing some of the basic combinatorial functions. Namely, the combination and permutation function. How do you properly pronounce $nCr$ and $nPr$?

Camelot823
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  • And how is $\binom{n}{r}$ (which is the equivalent of $nCr$) pronounced ? – Jean Marie Nov 20 '22 at 23:58
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    The binomial coefficient $\binom{n}{r} = nCr$ is often read as "$n$ choose $r$". – N. F. Taussig Nov 20 '22 at 23:59
  • I would call the corresponding buttons on a calculator the Choose and Permute buttons. I've never heard a good short name for ${}^n P_r$ for actual values of $n$ and $r$, I'd just call it "the number of permutations of $r$ objects from $n$ objects" formally, or "$r$ ordered choices of $n$ objects" informally. I've only ever really seen the number of permutations used in examples like counting words, where there's usually some concrete thing you can say instead of "objects" (like "letters" or "people"). – 1Rock Nov 21 '22 at 00:18
  • Apparently (https://math.stackexchange.com/questions/3022884/why-are-permutations-npr-called-variations-in-non-english-languages?rq=1), ordered choices of $r$ objects are actually called "$r$-permutations of $n$ objects". – 1Rock Nov 21 '22 at 00:20

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As others have noted, the binomial coefficient $nCr = \binom{n}{r}$ is pronounced "$n$ choose $r$."

The "falling factorial" $nPr = (n)_r = r!\binom{n}{r}$ can be pronounced "$n$ to the $r$ falling.": https://en.wikipedia.org/wiki/Falling_and_rising_factorials#Alternative_notations

RobPratt
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