If you decide to use a logo design with the Facebook logo included, you'll need to receive permission from Facebook first: https://www.facebook.com/brandpermissions/logos.php

Number six in the guidelines suggests that using the Facebook brand will not be approved:

"6.  You may not combine our Brand Assets, or elements of our Brand Assets, with your own name or mark or generic terms."

Sorry to put a damper on the contest, but I thought I'd pass this information on before anyone else includes the Facebook brand in their entries.