Definition:Binomial Coefficient/Technical Note

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Definition

The $\LaTeX$ code to render the binomial coefficient $\dbinom n k$ can be written in the following ways:

\dbinom n k

or:

\displaystyle {n \choose k}


The \dbinom form is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$ because it is simpler.

It is in fact an abbreviated form of \displaystyle \binom n k, which is the preferred construction when \displaystyle is required for another entity in the expression.

While the form \binom n k is valid $\LaTeX$ syntax, it renders the entity in the reduced size inline style: $\binom n k$ which $\mathsf{Pr} \infty \mathsf{fWiki}$ does not endorse.


To render compound arguments, braces are needed to delimit the parameter when using \dbinom, but (confusingly) not \choose.

For example, to render $\dbinom {a + b} {c d}$ the following can be used:

\dbinom {a + b} {c d}

or:

\displaystyle {a + b \choose c d} $\displaystyle {a + b \choose c d}$

Again, for consistency across $\mathsf{Pr} \infty \mathsf{fWiki}$, the \dbinom form is preferred.