I need to write a bijective proof for the following. I just don't know how to start. Any suggestions. Yes, it is due tonight. It is my last problem of my homework.

Find out how many how many sequences of subsets (Subscript[X, 1],Subscript[X, 2],..., Subscript[X, k]) of [n] are there that satisfy Subscript[X, 1]\[Intersection]Subscript[X, 2]\[Intersection]...\[Intersection]Subscript[X, k]=\[EmptySet] ?

Thanks in advance.