Generate N random numbers within a range with a constant sum

Question

I want to generate N random numbers drawn from a specif distribution (e.g uniform random) between [a,b] which sum to a constant C. I have tried a couple of solutions I could

Answer 1

well, for n=10000 cant we have a small number in there that is not random?

maybe generating sequence till sum > C-max reached and then just put one simple number to sum it up.

1 in 10000 is more like a very small noise in the system.