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dbinom

Displays binomial coefficients in a vertically stacked format, commonly used to represent combinations and probability calculations.

Overview

Essential for expressing combinatorial mathematics and probability theory calculations in a clear, professional format.

  • Widely used in probability distributions, particularly for binomial probability mass functions
  • Common in statistical formulas and combinatorics proofs
  • Preferred over \binom when working with discrete probability notation
  • Produces identical output to \binom but semantically indicates discrete probability contexts
  • Particularly useful in advanced statistics and discrete mathematics textbooks

Examples

Calculate the number of ways to choose k items from n items.

(nk)=n!k!(n−k)!\dbinom{n}{k} = \frac{n!}{k!(n-k)!} 
\dbinom{n}{k} = \frac{n!}{k!(n-k)!}

Probability mass function for a binomial distribution.

P(X=k)=(10k)pk(1−p)10−kP(X = k) = \dbinom{10}{k}p^k(1-p)^{10-k} 
P(X = k) = \dbinom{10}{k}p^k(1-p)^{10-k}

Expansion of a binomial coefficient in Pascal's triangle.

(42)=6\dbinom{4}{2} = 6 
\dbinom{4}{2} = 6