In combinatorics , a Rencontres number ( French: encounters ) is the number of permutations of a set of distinguishable elements designated with, in which elements exactly retain their original place or “find” again purely by chance:
.
In the event that none of the elements retains its place and "finds", arises as a special case, the Subfakultät , a formula for the number of possible fixed point free permutations (also derangements or "Total transfers") of elements in which so none of them at remains in its previous place:
.
example
A car owner cleaned the engine of his new four-cylinder and forgot to make a note of which of the four ignition cables goes on which spark plug. How many ways are there to reconnect exactly two of the four cables?
In detail: .
A year later, the same thing happened to him with the engine of his new six-cylinder. How many possibilities are there to put exactly half of the ignition cables back on?
literature
Dieter J. saddle roof: biomathematics I . Akademie-Verlag Berlin, 1971, ISBN 3-528-06083-2 , pp. 37-40.