Each student in a class of size n was born in a year with 36

Each student in a class of size n was born in a year with 365 days, and each reports his or her birth date (month and day, but not year).

(a) How many ways can this happen?

(b) How many ways can this happen with no repeated birth dates?

(c) What is the probability of no matching birth dates?

(d) In a class of 23 students, what is the probability of at least one repeated birth date?

Solution

a) 365! i.e 365 * 364 * 363 *....*1 b) 365 times c)1/365 d)1-1/23=22/23