# We Got A Problem #13: The Birthday Problem

July 28, 2013 Leave a comment

At my son’s recent 5th birthday party, he got 15 birthday cards. Sure enough, he got more than one of the same card.

Suppose everyone buys their cards at Foyerjohn, and randomly picks one of the cards. How many *different* cards would need to be on sale for there to be a 50% chance that all 15 people pick a distinct card?

*Harder:* how many different cards would need to be on sale for there to be a 50% chance that my son doesn’t get *three* of the same card?