Formula to Create a Partial List from a Complete List

I tried to use the Lookup(Max but that apparently works only for dates. My example is set up based on this attempt and may not be the best way to do what I am trying to do.

Column B is a complete list of personnel qualified to do a job. Checking the associated blocks means they are not available. Based on that information, I want to populate a list of personnel available in column F with no gaps so I can reference the "Available" list in another formula to auto-populate a calendar for scheduling.