You can surely put them in the same PC, but you are limited to a certain range of use cases:
- You can run screens from all of them. Im not entirely sure, but I believe Windows supports up to 256 monitors at the same time and displays up to 16 in the display properties window in the control panel.
- You can use them for distributed computing and/or render tasks.
- There are ways to run the AMD card as your primary display driver while using the nVidia card for PhysX
- With DirectX 12 it possible to use all devices able to render 3D environments like games together. That includes graphics card from AMD, nVidia and even the integrated solutrions from Intel. But the game/program has to actually support it.
What you can NOT
- Run them together in a multi-GPU config like Crossfire or SLISwitch between them as means of power saving like in some notebooks.
- Switch the cards to use the one that performs better in a certain game. (On Windows XP it would be possible to have two different hardware configurations, which you could switch via a reboot)