Permutation and Combination

permutation

${}_n \mathrm{ P }_k$

{}_n \mathrm{ P }_k

To write a small letter in the lower left corner, use "{}_". "P" is Roman type.

combination

${}_n \mathrm{ C }_k$

{}_n \mathrm{ C }_k
factorial

$n!$

n!
binomial coefficient

$\binom{ n }{ k }$

\binom{ n }{ k }

\binom comes from "binomial coefficient".係数）に由来しています。

binomial coefficient 2

${ n \choose k }$

{ n \choose k }

\choose is used to choose k from n. The braces are necessary to separate it from the preceding and following characters.

binomial coefficient 3

$\dbinom{ n }{ k }$

\dbinom{ n }{ k }

This is \binom in displaystyle.

repeated combination

${}_n \mathrm{ H }_k$

{}_n \mathrm{ H }_k
combination sample

$\begin{eqnarray} {}_n \mathrm{ C }_k = \binom{ n }{ k } = \frac{ n! }{ k! ( n - k )! } \end{eqnarray}$

\begin{eqnarray}
{}_n \mathrm{ C }_k
= \binom{ n }{ k }
= \frac{ n! }{ k! ( n - k )! }
\end{eqnarray}
permutation sample

$\begin{eqnarray} {}_n \mathrm{ P }_k = n \cdot ( n - 1 ) \cdots ( n - k + 1 ) = \frac{ n! }{ ( n - k )! } \end{eqnarray}$

\begin{eqnarray}
{}_n \mathrm{ P }_k
= n \cdot ( n - 1 ) \cdots ( n - k + 1 )
= \frac{ n! }{ ( n - k )! }
\end{eqnarray}
Formula
Symbol
Text
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