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A091715
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Numerator Q of probability P=Q(n)/365^(n-1) that three or more out of n people share the same birthday.
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2
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1, 1457, 1326781, 966556865, 616113172585, 359063094171965, 196176047915944825, 102076077386001384485, 51120278427593115164425, 24824896058243745467563925, 11753675337747799989826426225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| A 365 day year and a uniform distribution of birthdays throughout the year is assumed. The probability that 3 or more out of n people share a birthday equals the probability A091674(n)/365^(n-1) that 2 or more share a birthday minus the probability A091673(n)/365^(n-1) that exactly 2 share a birthday.
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LINKS
| Patrice Le Conte, Coincident Birthdays.
The Math Forum (AT) Drexel, Three Share a Birthday. Ask Dr. Math
Eric Weisstein's World of Mathematics, Birthday Problem. Section in World of Mathematics.
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FORMULA
| a(n)=A091674(n)-A091673(n)
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EXAMPLE
| The probability that 3 or more people in a group of 10 share the same birthday is a(10)/365^9=102076077386001384485/114983567789585767578125~=8.87744913*10^-4.
The probability exceeds 50% for n>A014088(3)=88.
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CROSSREFS
| Cf. A014088, A091673 Probabilities for exactly two, A091674 Probabilities for two or more.
Sequence in context: A052237 A145529 A203393 * A206147 A035764 A107560
Adjacent sequences: A091712 A091713 A091714 * A091716 A091717 A091718
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KEYWORD
| frac,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 04 2004
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EXTENSIONS
| Broken links corrected by S. R. Finch (Steven.Finch(AT)inria.fr), Jan 27 2009
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