Arrangement

Reference work entry
DOI: https://doi.org/10.1007/978-0-387-32833-1_15
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Arrangements are a concept found in combinatory analysis.

The number of arrangements is the number of ways drawing k objects from n objects where the order in which the objects are drawn is taken into account (in contrast to combinations).

HISTORY

See combinatory analysis.

MATHEMATICAL ASPECTS

  1. 1.

    Arrangements without repetitions

    An arrangement without repetition refers to the situation where the objects drawn are not placed back in for the next drawing. Each object can then only be drawn once during the k drawings.

    The number of arrangements of k objects amongst n without repetition is equal to:
    $$ A_n^k = \frac{n!}{(n-k)!}\:. $$
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© Springer-Verlag 2008