A102263 Denominators of probabilities in gift exchange problem with n people.

1, 4, 36, 144, 1800, 43200, 705600, 705600, 2116800, 127008000, 23051952000, 6638962176000, 280496151936000, 31415569016832000, 471233535252480000, 471233535252480000, 54474596675186688000, 3268475800511201280000

Offset: 2

Author

Jerrold Grossman, Feb 17 2005

Keywords

• nonn
• frac

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.

Examples

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

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 2..389
• Math Forum at Drexel, A variant on the "Secret Santa"

Crossrefs

Cf. A102262, A136300.

Formula

See A102262 for formula for p(n).

Extensions

More terms from Jon E. Schoenfield, Sep 30 2006