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Decimal expansion of 1 - ((365!) / ((365 - 23)! * 365^23)).
1

%I #19 Jul 27 2022 02:16:50

%S 5,0,7,2,9,7,2,3,4,3,2,3,9,8,5,4,0,7,2,2,5,4,1,7,2,2,8,3,3,7,0,3,2,5,

%T 0,0,2,3,5,9,7,1,8,4,5,2,9,2,9,8,7,8,0,9,9,0,1,9,7,4,0,0,2,0,0,1,8,8,

%U 4,1,8,3,9,1,8,1,2,7,7,1,5,9,9,2,2,3,3,1,6,8,0,5,3,7,0,5,3,2,0,1,1,8,6,4,8,3,2,8,4,7,7,6,5,4,2,4,6,8,6,0

%N Decimal expansion of 1 - ((365!) / ((365 - 23)! * 365^23)).

%C This is the probability that at least two people in a room of 23 randomly selected people share a birthday, ignoring leap days and assuming days are equiprobable.

%C This is a rational number; numerator and denominator both have 53 digits. - _Charles R Greathouse IV_, Jul 11 2020

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>

%e 0.5072972343239854072254172283370325...

%t RealDigits[1- ((365!) / ((365 - 23)! * 365^23)), 10, 120]

%o (PARI) 1. - 364!/(342! * 365^22) \\ _Charles R Greathouse IV_, Mar 25 2020

%Y Cf. A014088, A343015.

%K cons,nonn

%O 0,1

%A _Kritsada Moomuang_, Mar 25 2020