For the iPads, you can use Apple Configurator to install apps on all 15 iPads using a single Apple ID. For paid apps, you will need to enroll in Apple's Education VPP program http://www.apple.com/education/volume-purchase-program/ which will allow a single Apple ID to purchase multiple licenses of an app. And best of all, you can save 50% of the cost on most apps when buying 20 copies or more. So even if you only need 15 licenses of a paid app, its cheaper to purchase 20 through VPP and save 50%. Using Apple Configurator, I would "Supervise" the iPads and install the apps (and configuration profiles) to all iPads.
Apple Configurator Resources
PDF: http://www.apple.com/iphone/business/docs/iOS_Apple_Configurator_Mar12.pdf
Video: http://www.apple.com/education/resources/videos/#introduction-to-apple-configura tor
Help Pages: http://help.apple.com/configurator/mac/1.0/
I'm not sure if they have a similar program to VPP for the OS X computers…
But the limit you are referring to is for a single personal Apple ID (not for multiple users) that is allowed to be associated with a total of 10 devices (up to 5 computers and the rest on iOS devices). Example you can have 5 computers and 5 iOS devices, 3 computers and 7 iOS devices, but not 6 computers and 4 iOS devices.
From http://www.apple.com/legal/itunes/us/terms.html#SERVICE
Association of Associated Devices is subject to the following terms:
i) You may auto-download iTunes Auto-Delivery Content or download previously-purchased iTunes Eligible Content from an Account on up to 10 Associated Devices, provided no more than 5 are iTunes-authorized computers.
Again this is for a single user. For multiple users like in schools you need to use VPP to purchase multiple licenses and it will allow you to install on multiple devices using a single district Apple ID.
Hope this helps!
~Joe
