Hi Tony,
first off the concept of classful IP addressing is deprecated (god I sound like a book)... in other words, everyone uses classless routing now, because using the classes became very wasteful.
You can use any mask you like with any 'class' as such.. especially so if its an internal network IP. Remember the mask just divides the host ID and network ID sections of the IP address. If you were using classful addressing you'd have the following :
10.0.0.0
255.0.0.0
But since your admin isn't bothered about the class, you've got whats technically a class A IP space subnetted with a class C mask. This is fine. In fact its exactly what you said it was -- 'A class A IP range with Class C subnets'.
Furthermore, this is from the 'private' class A address space. In other words you use these IP's internally, you cannot route these IP's over the Internet. The following are the private IP spaces :
Class A - 10.0.0.0 - 10.255.255.255
Class B - 172.16.0.0. - 172.31.255.255
Class C - 192.168.0.0 - 192.168.255.255
If you want to read about private addressing, its covered in RFC1918, you can find it here :
www.cis.ohio-state.edu/cgi-bin/rfc/rfc1918.html
Hmm I'm running on very little sleep so forgive if that explanation wasn't very good. I actually find the explanation we have up here on the site very good. It does not confuse the topic and you can visualise things better. Print it out and give it a read.
As a motivational tip, subnetting is not hard -- even if you're bad at math.. its all about a mental block. Focus on the concept rather that the actual method you're using... because there are lots of tips and tricks.. everyone has their own way of working subnets out. Check the Certification / Books & More forum, there should be a post in there called 'Subnetting tricks', which has some contributions from the members.
Default subnet mask is for class C network. Just playing around and no one knows what they are doing it is just going to be for a class "C" .... 
