In a group of 30 people, must at least 3 have been born in the same month? Why?

Question

This is a pigeon hole principle problem and I'm not sure how I can word this to prove that at least 3 have been born in the same month out of 30 people?

Answer 1

Suppose , Month is Box and person is ball. Total Box is 12 and Ball is 30. Up to 24 Ball you can distribute in the box so that no Box contain more than 2 Ball.

You can put 2 Ball in each Box.But it is Impossible to add more Ball (25 Ball) so that any Box does't have more than 2 Ball. So If it impossible for 25 Ball, it is also impossible for 30 Ball.

Answer 2

If no three persons were born in the same month, then you could have at most two born in January, two born in February and so on for a total of 24. Since there are more than 24 people, it is impossible that no three persons were born in the same month.