I'm thinking of making my african american intern work on mlk jr day? she was one of three picked at random
I'm kind of struggling to understand why you would want to force someone to work on mlk jr day?
Because I think its a good idea.
If everyone else works at the office that day, it's fine to ask african americans to do so as well.  Everyone should work when they're expected to.
What if I want my interns to work on that day.
It is fine to make people work if they were chosen to work for that day, and you are well within your right. However, I am not sure why you need to bring up that they are African American and that it is MLK Jr. Day.