1. Let $m, n \in \mathbf{N}_{+}$, and $m>n$, sets $A, B, C$ satisfy
$$
\begin{array}{l}
A=\{1,2, \cdots, m\}, B=\{1,2, \cdots, n\}, \\
C \subseteq A, B \cap C \neq \varnothing .
\end{array}
$$

Then the number of sets $C$ that meet the conditions is $\qquad$
$$
-1.2^{m-n}\left(2^{n}-1\right) \text {. }
$$

From the condition, we know that the elements of set $C$ partly come from the non-empty subsets of set $B$, which have $2^{n}-1$ ways of selection; the other part comes from the set $\{n+1, n+2, \cdots, m\}$, which has $2^{m-n}$ ways of selection. Therefore, there are a total of $2^{m-n}\left(2^{n}-1\right)$ ways of selection.