How to Count for each category

This should be relatively simple, but I think I am over thinking it.

In the attached spreadsheet, I have words broken out into 3 categories (person, place, thing).

Next to each word, there is also a number. What I am looking to do is:

IF the number is between 1-5 and IF its within the Category People, THEN count how many there are
also
IF the number is between 6-10 and IF its within the Category People, THEN count how many there are...
Etc, for each category.

Like I said, this should be simple, but I am having a brain fart.

Thanks for the help!
Aaron