Oops! Thanks, just distraction... It's that first I wanted to see the general solution to those kind of problems (and I gave the solution for a wrong one in the class), then I wanted to verify the C implementation of the solution with POPCNT like the OP seems to have done (I am writing the code)...

Edit: ...and yes, it seems that brute-forcing (counting to one trillion) takes more time than I expected.

Now I see it. Twenty items (R operations) in 40 slots: 40!/(20!) and the order of the items does not matter, so again divide by 20!. The remaining slots are D operations.

The answer actually came to me in the shower this morning.