I need to simulate a random initial state of an 1D cellular automaton, but with different 'densities' of filled cells.
Let's say the size of the list is $N$, then I need to be able to fix a number $P$ such that there are exactly $P$ $1$s and $N-P$ $0$s.
RandomInteger gives $1$s or $0$s with probability $p=1/2$, but first, I still din't work out how to correctly modify the probability so it can change from $0$ to $1$, and second, I would prefer for the number to be exact.
In other words, I have $P$ $1$s and $N-P$ $0$s and I need to randomly and uniformly distribute them inside a singe list. I'm not sure how to do that efficiently.
I suppose I could create a list of all the possible positions and use
RandomSample[list,P] to fill them with $1$s. But is there a better way?
Important point! $N$ will be very large (up to 100 000).