Per User Remote Desktop Licensing

I want to be sure I understand how the per user Remote Desktop licensing works.  Below is my example.

I have an Active Directory with 3 Remote Desktop servers and another server acting as the Domain Controller and Remote Desktop License Server.

The network is a single domain.

All servers use the same Remote Desktop license server.

All Remote Desktop licenses are per user.

If I have 10 users, do I need 10 Remote Desktop licenses per server or just 10 Remote Desktop licenses?

There are 10 specific people on the network.

If I understand it correctly only one Remote Desktop license server is needed.

All servers use the one Remote Desktop license server.

I think only 10 Remote Desktop CALS are needed and NOT 10 Remote Desktop CALS per server.

My one CAL would give me the rights to log into any of the 3 Remote Desktop servers I need to access.

Is this correct?