A091715 Numerator Q of probability P = Q(n)/365^(n-1) that three or more out of n people share the same birthday.

1, 1457, 1326781, 966556865, 616113172585, 359063094171965, 196176047915944825, 102076077386001384485, 51120278427593115164425, 24824896058243745467563925, 11753675337747799989826426225

Offset

3,2

Comments

A 365-day year and a uniform distribution of birthdays throughout the year are 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.

Links

Table of n, a(n) for n=3..13.

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.

Formula

a(n) = A091674(n) - A091673(n).

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.

Crossrefs

Cf. A014088, A091673 (probabilities for exactly two), A091674 (probabilities for two or more).

Sequence in context: A351549 A235554 A255345 * A224528 A206147 A035764

Adjacent sequences: A091712 A091713 A091714 * A091716 A091717 A091718

Keyword

frac,nonn

Author

Hugo Pfoertner, Feb 04 2004

Status

approved