Question

Show that if eight people are in a room, at least two of them have birthdays  that occur on the same day of  the week.

Answer 1

The Pigeonhole Principle: If $n + 1$ objects are placed into $n$ boxes, then some box contains at least 2 objects. 

There are $n=7$ days(‘boxes’), but we have $n+1 = 8$ people (‘objects’). Therefore at least two of eight people have birthdays  that occur on the same day of  the week.