Pigeonhole Principle: Theorem and Examples

In this video, a brief introduction to the Pigeonhole Principle is given.
There are three examples:
1, A busy airport sees 1500 takeoffs per day.
Prove that there are two planes that must take off within a minute of each other.'

2, Prove that every year contains at least four and at most five months that contain five Sundays.

3, A college has 39 departments and a total of 261 faculty members in those departments. Prove that there are three departments in this college that have a total of at least 21 faculty members.

Thanks for watching!