Have you tried booting to internet recovery?
Command-OPTION-R
at boot
You'll need your wifi password (unless you plug it into ethernet).
The utilities take a while to load, be patient as the globe spins.
When the utilities are loaded, open disk utility.
IMPORTANT: check to see if there's a "view" menu.
If there IS, you MUST go to it and choose "show all devices".
Look at the list on the left.
The topmost item is the internal drive.
We need to erase it.
Click on it and click erase.
Choose "Mac OS extended, journaling enabled, GUID partition format".
When the erase is done, quit disk utility and open the OS installer.
Start clicking through. The Mac will reboot one or more times, and the screen will go dark for up to a minute with no other indication of activity. Be patient.
When done, you should see the initial setup screen "choose your language".
If you get this far successfully, the final step is to press and hold the power-on button CONTINUOUSLY until the screen goes dark and the Mac shuts off.
It's now ready to hand over to the person who's getting it.
One final thought:
You should tell the recipient that the 2011 MacBook Pro 15" and 17" models are subject to "RadeonGate" (GPU failure), and that it could fail at any time.
It's no longer something that is "repairable".
It's possible to disable the discrete GPU and run with only the integrated GPU -- there are threads in this forum on how to do that.
