Note that SRSWOR refers to Let U be a population of size N. From U, we first select a Simple Random Sample Without Replacement (SRSWOR), S_1 , of size n_1 . Then, from S_1 , we select a SRSWOR, S_2 , of size n_2 . Show that S_2 is a SRSWOR of size n_2 selected from U.
I wasn't familiar with the notion of SRSWOR. But during my research I found that the probability of selecting S_1 for example is P(S_1)= 1/[N!/n_1!(N-n_1)!] I also thought that the answer deals with the fact that S_2 depends actually on S_1? I explored the path of conditional probability and proof for inclusion and subset.
This is a two-phase Simple Random Sampling Without Replacement (SRSWOR). the SRSWOR, $S_2$ of size $n_2$ has been chosen from $S_1$ which is a SRSWOR of size $n_1$ drawn from U. We can see the Sample $S_2$ as a set which is a subset of $S_1$, and also $S_1$ a subset of U. Then $S_2$ is also a subset of U. So the second phase of the sampling which requires to draw $S_2$ of size $n_2$ from $S_1$ is equivalent to a one phase sampling which requires to draw $S_2$ of size $n_2$ from the original set U. Therefore we can then conclude that $S_2$ is a SRSWOR of size $n_2$ selected from U.