How many ways are there to choose an arbitrary number of students (including the possibility of choosing 0 students) from 6 students?

Question

I'm a little confused by the wording of this question, more specifically "an arbitrary number".

Is the answer to this 6!? Or simply 7?

Thanks!

Answer 1

To add to the answers in the comments note that if the set of students is given by $S = \{1,2,3,4,5,6\}$ then the question similarly asks what is the number of subsets of $S$. From the definition of the power set we know this to be $2^{|S|}$.

This is also a neat combinatorial argument for why $$2^n = \sum_{i=0}^n {n \choose i}.$$ An alternative way of proving this formula is with the Binomial Theorem by choosing $x=y=1$.