Suppose that n people are selected at random from the engine

Suppose that n people are selected at random from the engineering programs. What is the chance that at least two of those n were born on the same day? (Leap years omitted)

Solution

Note that

P(at least 2 have the same bday) = 1 - P(all have distinct bday)

There are 365Pn ways for them to have distinct bdays, and 365^n total ways for them to have any birthday.

Thus,

P(at least 2 have the same bday) = 1 - (365Pn)/(365^n)

where 365Pn = 365!/(365-n)!, and n <= 365.