antivurs expired, getting a new one

I've had Norton Antivirus for a year, and it's worked well for me.  I have been getting these popup messages to renew and upgrade to the 2011 product, but it seems more expensive than buying a brand new copy.  so i ordered a new antivurs - it says for 3 computers.

 

1st Q -  should i use the removal tool to completely delete the old one before i put the new disc in or will it just know that i already have the 2010 expired version on my hard drive

 

2nd Q - so it says i can use this on three computers, seems like a pretty good deal to me.  so i am going to be able to install this new disc on 3 computers and Norton will know (via online updates i suppose), that i am only putting it on 3 computers and not more?  as my other nortons expire i plan on putting this new disc on it.