Combinatorics

Permutations:
The number of arrangements of r out of the n objects, with order importance:

(1)
\begin{align} P_r^n = \frac{{n!}}{{(n - r)!}} \end{align}

Example: the number of permutation r=2 out of n=3 equals 6: ab,ac,ba,ca,bc,cb

The number of permutations of n objects divided to k groups with ni sizes. The objects within the group are the same.

(2)
\begin{align} \frac{{({n_1} + {n_2} + ... + {n_k})!}}{{{n_1}!{n_2}!...{n_k}!}} \end{align}

Example:

Combinations:
The number of arrangements of r out of the n objects, without order importance:

(3)
\begin{align} \left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right) = \frac{{n!}}{{r!(n - r)!}} \end{align}

Example: ab,ac,bc - 2 out of 3 gives 3

page revision: 10, last edited: 02 Feb 2013 19:34