Group Assignment

Chef is hosting a party at his house and $N$ people are invited to it. Everyone has arrived and they are eager to make a group and chit-chat. The $i^{th}$ person prefers to be in a group of **exactly** $P_i$ people (including himself). A person who is not in a group of preferred size gets upset. Find whether Chef would be able to assign every person to a group such that everyone remains happy. #