# Is sampling from a discrete distribution of known size random number of times with random probability distribution equivalent to a random sampling?

What I mean to ask is if I have to choose a random number of elements(say 3) without replacement from a set(for example {1,2,3,4,5,6,7}) with a probability distribution generated by running a pseudo random number generator number of times equal to the size of the set and normalized to summation of 1. Is this equivalent to choosing a random number of elements from the same set without replacement? Are their any biases that happen?