Counting how often a term of a taxonomy has been used.

On one of my websites I am trying to do the following. I’ve got a several custom taxonomies, like companies and schools. The terms in these taxonomies are several companies and schools in the area.

I’ve made this so I can:

1. attach these companies and schools to posts
2. so that on a company-page or school-page on the same site I can list all the posts that mention that company or school very easily.

Now I am looking for a way to count how many times a term has been attached to a post, anywhere within the site. I need to know this so I can hide the list and title in question on the company-page or school-page.