Doubt in week 18 : probability Space

Look at the top right in the attached image circled in red, does the number of samples which are to be mapped by a random variable is equal to the number of samples in the sample space (omega) i.e all possible samples of size n? if yes then how is this feasible coz at the first place we can’t compute parameter for the entire population then how can we take all possible samples i.e N C n .If No, then suppose the number of samples for mapping with Random variable is k (k< N C n) , then while plotting the probability distribution what must be the probability of each such k samples: 1/k or 1/(N C n) coz in the latter case the summation of probability of all k samples will be k/(N C n) and not 1.