If you are talking about Office 2010, you are apparently incorrect:
Can I install Office Home and Business 2010 and Office Professional 2010 on more than one PC?
It depends on what you purchase—a Traditional Disc or Product Key Card. If you purchase a Traditional Disc retail license of Office Home and Business 2010 or Office Professional 2010, the retail license terms allow you to install, activate, and use Office Home and Business 2010 or Office Professional 2010 on your primary PC and your portable device such as your laptop. This license is for your use exclusively.
If you purchase an Office 2010 Product Key Card, you can only activate and use the suite on one PC or device. For more information on the license you have purchased and to obtain an overview of your licensing agreement, visit the Microsoft Software License Terms (MSLT)
I thought when I bought Microsoft Office Student and Teacher Edition there were 3 installations possible. I have only used 2 of them and I wish to know if I am correct.
As I recall, when I purchased the same software for my daughter when she went to college a couple of years ago, it did indeed come with 3 product keys for up to 3 installations. Really a matter of what particular version you purchased. Good luck!