Cable requirements for new home

Contractor plans to install cable to 3 locations of my choice for 3 TVs.  On Cox web site it says a cable is also required for the internet modem/router so, if true, I think I need 4 cables. Is this right or can 1 cable be used for 1 of the TVs and the internet equipment at the same time?  

I'm trying to figure out where the internet equipment and DVR receiver will be located.  Are the 2 connected by a cable directly?  Can they be in separate locations if you run a cable between the 2?  Just want to get it right before the walls are closed up.