question about sets and subsets using the definition 
Assume $A$ and $B$ are two sets such that: $Card(A)=n$ and $Card(B)=m$, also $B⊆A$,Clearly $n\ge 
m$.
  define: $$\mathscr{P}(A:B)=\left\{X∈\mathscr{P}(A):B⊆X\right\}$$
  find the number of elements of $\mathscr{P}(A:B)$

I just know $Card\left(B\right)\le Card\left(X\right)$
how I can answer the question?
does there exist any general formula?

Below, a reasoning ( probably not a proof properly speaking) trying to answer the question : in how many ways can one " build" a set X belonging to P(A:B). The number of possible ways to build a member of P(A:B) is the same as the number of members of P(A:B). 

