How many ways are there for a bank to choose n students? A bank comes to campus and interviews each person one at a time. After each interview they decide to hire that person or not. i. There are n students. How many decisions does the bank make? ii. How many ways are there to choose students to get jobs at the bank? I am confused about this. I think on the first one that maybe we let k be the number of decisions the bank makes. Since there are n students and the bank makes k decisions, we have $\binom{n}{k}$. And isn't the second one identical to the first one? Or maybe it's just $2^{n}$ ways to choose students to offer jobs at the bank?

I believe that this is overthinking it a bit.

i. There are n students, and each student is a yes or no, leaving n decisions

ii. Every student has 2 options (yes or no), leaving $2^n$