Generate vector of random variables with constraints

What's an efficient way to generate N unique vectors of length M (each element a random variable drawn from its own arbitrary distribution pmf_m) so that each vector satisfies two rules:

1. Elements are unique
2. Elements are integers bounded in the interval (0,M]

For context- I'm performing a Monte Carlo simulation relying on M competitors' rankings after a contest as input, but want to consider only realistic outcomes by modeling the likelihood of each one's placement based on a measure of their skill.