How long does it take for his permanent tooth to come in after his baby tooth falls out?

Usually quickly: It depends on the situation. Some teeth are lost and the permanent one doesn't appear for years, usually it is right there as soon as the baby tooth falls out. A check up with an orthodontist or pediatric dentist can easily identify if there is a problem.

Just depends: Some teeth come in before the baby tooth falls out and others can take a month. You should see a dentist to make sure the adult tooth is there and is erupting properly.