Efficient random permutation of n-set-bits

Question

For the problem of producing a bit-pattern with exactly n set bits, I know of two practical methods, but they both have limitations I\'m not happy with.

Fir

Answer 1

I would use solution number 3, generate the i-th permutation.
But do you need to generate the first i-1 ones?

You can do it a bit faster than that with kind of divide and conquer method proposed here: Returning i-th combination of a bit array and maybe you can improve the solution a bit