9 people are assigned to one of 17 posts uniformly at random and more than one person can be at one post. Letting $X$ be the random variable representing the number of occupied posts, I was tasked with computing the expectation.
For my sample space $\Omega$, I was thinking of doing tuples where a person is mapped to one of the 17 posts with $|\Omega|=17^{9}$ (by stars and bars).
From here on I'm always confused with expectation. Would it be beneficial to utilize indicator random variables or do I have all I need to solve this?
Yes, it is simplest to use indicator random variables and the linearity of expectation.
Let $X_i$ equal one if post $i$ is occupied and zero otherwise. $X$, the count of occupied posts is then the sum of the seventeen indicators. $$\mathsf E(X)=\mathsf E(\sum_{i=1}^{17}X_i)$$