Most efficient method of generating a random number with a fixed number of bits set

Question

I need to generate a random number, but it needs to be selected from the set of binary numbers with equal numbers of set bits. E.g. choose a random byte value with exactly 2

Answer 1

Say the number of bits to set is b and the word size is w. I would create a vector v of of length w with the first b values set to 1 and the rest set to 0. Then just shuffle v.