Arrangement

HISTORY

See combinatory analysis.

MATHEMATICAL ASPECTS

• 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:

  $$ A_n^k = \frac{n!}{(n-k)!}\:. $$

• 2. Arrangements with repetitions

  Arrangements with repetition occur when each object pulled out is placed back in for the next drawing. Each object can then be drawn r times from k drawings, ${ r = 0, 1, \ldots, k }$.

  The number of arrangements of k objects amongst n with repetitions is equal to n to the power k:

  $$ A_n^k = n^k\:. $$
  ...