Shared Birthdays

Why do birthday coincidences spring up in medium sized groups of people?

Is it rare or common to find several persons share the same birthday?

How frequent do these coincidences occur for small groups (20-30 persons)?

But the year has 365 days! Ample room for each one to have its own day!

Shouldn't it be rare for small groups to have these coincidences? So...

How frequent is that at least persons in a group of share the same birthday?
Let's Find Out !