How many people must be in a room so that at least 10 have a birthday on a Friday?
edit: Assume that no two people share the same birthday
I'm somewhat confused and see two different ways to solve the problem. First, since all birthdays fall on one of seven days, if there are 64 people in the room one would at least one day of the week to hold 10 people. This is a similar problem: picking certain number of days.
However, there are 366 possible birthdays and only 52 or 53 of those are Fridays, giving $\displaystyle366 - 52= 314$ days of the year that are not Friday. So to be absolutely certain there are 10 people with Friday birthdays, would one need $314+10=324$ people?