Binomial coefficients in LaTeX
A binomial coefficient counts the ways to choose k items from n; in LaTeX \binom{n}{k} typesets 'n choose as a bracketed column with no fraction bar.
LaTeX command
\binom{n}{k}Not the symbol you meant? Draw it to find the command →
The command \binom{n}{k} takes the top value first and the bottom second, drawing them inside parentheses with no dividing line. This is what distinguishes it from \frac, which draws a bar. \binom comes from amsmath and is supported by KaTeX. It reads aloud as 'n choose .
Size variants mirror the fraction commands: \dbinom forces the large display style inline, and \tbinom forces the small style inside a display. The older plain-TeX form {} still works and gives the same output, but \binom is clearer and preferred in modern documents.
Binomial coefficients appear throughout combinatorics and the binomial theorem, so they often sit next to sums and factorials. Because \binom is a single unit, it nests cleanly inside sums such as \sum_{k=0}^{n} \binom{n}{k}, and its parentheses grow automatically with the content.
Other forms
\dbinom{n}{k}display size inline{n \choose k}older \choose formExamples
$\binom{n}{k} = \frac{n!}{k!(n-k)!}$the definition in terms of factorials
$\binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k}$Pascal's rule
$(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$the binomial theorem
$\dbinom{n}{k}$the display-size form used inline
Tips and common mistakes
\binomneeds amsmath in a full document; KaTeX supports it natively.- Do not build a binomial with
\frac; that adds a fraction bar.\binomdeliberately has none. - Use
\dbinomfor a larger coefficient in running text and\tbinomfor a smaller one inside a display. - The old {} form still works but is discouraged; prefer
\binom{n}{k}. - Both arguments are groups, so multi-token values like
\binom{n-1}{k-1}need no extra braces around the whole thing.
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Convert your maths to LaTeX →FAQ
How do I write 'n choose in LaTeX?
Use \binom{n}{k}. The first argument is the top number, the second is the bottom, and the result is set in parentheses with no bar.
What is the difference between \binom and \frac?
\frac draws a horizontal bar between the two arguments; \binom does not, which is exactly what a binomial coefficient needs.
How do I make a display-size binomial inline?
Use \dbinom{n}{k}, the binomial counterpart of \dfrac. For a small binomial inside a displayed equation, use \tbinom{n}{k}.