8

Any reason to prefer one over the other? Or are they exactly the same?

  • 3
    The result should be exactly the same, but \binom is defined in LaTeX terms, with two arguments, explicitly delimited in braces. \choose, on the other hand, is plain TeX and requires more care in its input, since its beginning and end are not clear. The result may not be what's expected. (I'm not sure; \choose may by now have been "disabled" in LaTeX.) – barbara beeton Jun 27 '23 at 02:25
  • 1
    @barbarabeeton It's not disabled. With amsmath you get a warning about “Foreign command \atopwithdelims” (which is a bit unclear…), essentially because \choose is \atopwithdelims() – egreg Jun 27 '23 at 09:49
  • For a related discussion, see What is the difference between \over and \frac? – Mico Jun 27 '23 at 15:18

1 Answers1

18

  • \choose is a plain-TeX math-mode macro. Syntax: {n-k\choose k}. Note that the macro uses TeX's (in)famous infix syntax.

  • \binom is a LaTeX math-mode macro provided by the amsmath package. Syntax: \binom{n-k}{k}. No infix syntax here; instead, two explicit arguments.

  • A comparable distinction arises between plain-TeX's \over directive, to be used as {a+b\over c+d}, versus LaTeX's \frac macro, to be used as \frac{a+b}{c+d}. If you're not used to TeX's infix notation syntax, you're probably better off sticking with the LaTeX macros.

  • Just like the amsmath package provides \dfrac and \tfrac as display-style and text-style companions to \frac, the package also provides the macros \dbinom and \tbinom as companions to \binom. There is no equivalent one-letter modifier for \choose or, for that matter, \over.

  • When used appropriately, both \choose and \binom should give exactly the same result. Emphasis on appropriately. As always, if you know what you're doing, there's no real downside to using \choose along with its infix syntax. In contrast, if you're not in that group, using \binom (or \tbinom or \dbinom) is probably the way to go.

Mico
  • 506,678
  • 2
    +1, of course. The net is plagued with expressions such as “x-1/x+1”, which stem from the practice of saying “x minus one over x plus one”, which may be clarified in speech by appropriate pauses: “x minus one (pause) over (pause) x plus one”, compared to “x plus (pause) one over x (pause) plus 1”. The TeX primitive syntax has no counterpart for those pauses and this is its main fault. – egreg Jun 27 '23 at 09:57
  • 3
    @egreg -- Braces are the counterpart of the pauses, but of course braces are only visible, not audible. (And, of course, under some circumstances, can be omitted.) – barbara beeton Jun 27 '23 at 12:36