03. Combination

Combinations without putting back

Combinations are the number of possible subsets out of a set (note: not ordered; if it were ordered, that would be called Variation).

The number of possible combinations of taking 1 item out of a set of N items is N.

The number of possible combinations C of taking n items out of a set of N items (when putting them back only after taking all the n items) is:

$C=\binom{N}{n}:=÷{N!}{n!⋅(N-n)!}$

that is, "all!" divided by "good!"⋅"bad!".

$\binom{N}{n}=0,n>N$

$\binom{N}{0}=1$

$\binom{N}{1}=N$

$\binom{N}{N}=1$ (because we are talking of an set, which is unordered)

$n⋅\binom{N}{n}=N⋅\binom{N-1}{n-1}$

TODO

Author: Danny (remove the ".nospam" to send)

Last modification on: Thu, 09 May 2013 .