OFFSET

2,2

COMMENTS

n friends organize a gift exchange. The n names are put into a hat and the first person draws one. If she picks her own name, then she returns it to the bag and draws again, repeating until she has a name that is not her own. Then the second person draws, again returning his own name if it is drawn. This continues down the line. What is the probability p(n) that when the n-th person draws, only her own name will be left in the bag?

I heard about the problem from Gary Thompson at Grove City College in PA.

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 2..389

Math Forum at Drexel, A variant on the "Secret Santa"

FORMULA

See A102262 for formula for p(n).

EXAMPLE

p(2) through p(10) are 0, 1/4, 5/36, 19/144, 203/1800, 4343/43200, 63853/705600, 58129/705600, 160127/2116800.

CROSSREFS

KEYWORD

nonn,frac

AUTHOR

Jerrold Grossman, Feb 17 2005

EXTENSIONS

More terms from Jon E. Schoenfield, Sep 30 2006

STATUS

approved