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A091673
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Numerator Q of probability P=Q(n)/365^(n-1) that exactly two out of n people share the same birthday.
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2
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1, 1092, 793884, 480299820, 261163522620, 132358677731280, 63798093049771080, 29612552769907347240, 13345042642324219106280, 5872442544965392834838400, 2533775368098060137659608000, 1075256447734638237381213700800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| A 365 day year and a uniform distribution of birthdays throughout the year is assumed.
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LINKS
| P. Le Conte, Coincident Birthdays.
Eric Weisstein's World of Mathematics, Birthday Problem. Section in World of Mathematics.
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FORMULA
| P(n)=n!*sum_{i=1..floor(n/2)}(binomial(365, i)*binomial(365-i, n-2*i)/2^i)
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EXAMPLE
| a(3)=1092 because the probability in a group of 3 people that exactly two of them share the same birthday is (1/365^3)*3!*binomial(365,1)*binomial(364,1)/2=
(1/365^2)*3*364=(1/365^2)*1092.
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MATHEMATICA
| P[n_] := (n! Sum[ Binomial[365, i]*Binomial[365 - i, n - 2i] /2^i, {i, 1, Floor[n/2]}]/365); Table[ P[n], {n, 2, 13}] (from Robert G. Wilson v Feb 09 2004)
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CROSSREFS
| Cf. A014088, A091674 gives probabilities for two or more coincidences, A091715 gives probabilities for three or more coincidences.
Sequence in context: A043856 A043864 A043873 * A174422 A096082 A138698
Adjacent sequences: A091670 A091671 A091672 * A091674 A091675 A091676
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KEYWORD
| frac,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 03 2004
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EXTENSIONS
| More terms from Robert G. Wilson v, 9rgwv(AT)rgwv.com), Feb 09 2004
Broken links corrected by S. R. Finch (Steven.Finch(AT)inria.fr), Jan 27 2009
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