You can search for people with a given title, or a company that is in a specific industry, etc. You can do boolean searches and do pretty complex searches depending on your LinkedIn account (free, business, etc.).

For instance, you could find out how many companies are in the day care business in a specific state or in the US as a whole, etc. You could search for professionals with "day care" or "care taker" listed somewhere in their title or profile and do some basic guesses from there.