Fred.Bone at dial.pipex.com
Tue Sep 1 16:49:55 UTC 2009
On 01 September 2009 at 11:14, Robin Woolley said:
> Reading the late Paul Cattermole's obituary in the paper on Saturday
> reminded me of a problem he set some years ago. The problem was: How many
> derangements are there on n bells, where a derangement is a row with no
> bell in its own position?
The number of derangements of n items is (n!/e). The Wikipedia article on
derangements has a good derivation of this (basically, consider swapping
the nth item with the item that belongs in the nth place: the result can
be reduced either to a derangement of n-1 or one of n-2, in n-1 ways
each; then massage the recurrence relation).
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