Before running a quiz and contest you must be sure to be in compliance with both State Rules and the publisher that you are using.
Rules and guidance for Facebook contests are in this link. Facebook Rules
A Sweepstakes is a campaign in which entrants can win a prize based on chance. No purchase, payment, or other consideration is permitted, and the winner is picked at random. The element of consideration must not exist in a Sweepstakes. Caution: consideration is anything of value the contestant must give up to participate, monetary or non-monetary, and can exist if the contestant must expend substantial time or effort that benefits the sponsor. For example, some states have determined that providing contact information is consideration if the information is to be used for marketing purposes.
A Contest is a campaign in which effort, skill, or merit, is required to enter to win a prize.For example, you may require people to upload a photo or video in order to enter. The winner is determined by voting or other judging criteria. The element of chance must not exist in a contest.
A Lottery requires purchase, payment, or other consideration (the contestant has to buy something, such as a ticket), chance, and a prize. Private lotteries are illegal under state law. Moreover, under federal law, it is illegal for U.S. citizens to even participate in a foreign lottery. Do not run a lottery.