10. Given $A=\{1,2,3,4, \cdots, 2002\}, B=\{1,2,3, \cdots, 1000\}$. If $C \subseteq$ $A, B \cap C \neq \varnothing$, then the subset $C$ has $\qquad$ in total.
10. $2^{2002}-2^{1002}$.

Let $M=\{1001,1002,1003, \cdots, 2002\}$, then $A=B \cup M$, it can be known that the subsets of $M$ which have an empty intersection with $B$, there are $2^{1002}$ such subsets. Therefore, the number of subsets $C$ that meet the condition is $2^{2002}-2^{1002}$ (sets).