This month's Challenge Question: Specs & Techs from GlobalSpec:
A school teacher notices that 3 students in his class of 30
students share the same birthday. What is the percent chance of this occurring?
Assume all days of the year are equally likely as a birthday,
ignore leap years, and assume the class represents a random sample of birthdays.
And the answer is:
There is a 2.85% chance that three people among 30 share the
same birthday.
This problem is the triplet variation of the The Birthday Problem.
The equation to solve this problem is:
where W is the number of triplets present in the class (there could be more than one
set of triplets), n is the number of students in the class, and m is the number
of days in a year. [A.
DasGupta, J. Statist. Plann. Inference 130, 377 (2005)]

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