7. Alice has three daughters, and each of them has two daughters; Alice's six granddaughters each have one daughter. Then, the number of sets (including the empty set) formed by the women in these 16 families, where no one is in the same set as her daughter, is $\qquad$.


7. 2926

Analysis: We discuss in two cases: (1) If the subset contains Alice, then there are a total of $3^{6}$ subsets; (2) If the subset does not contain Alice, then there are a total of $C_{3}^{0} \cdot 3^{6}+C_{3}^{1} \cdot 3^{4} \cdot 4+C_{3}^{2} \cdot 3^{2} \cdot 4^{2}+C_{3}^{3} \cdot 4^{3}=13^{3}=2197$ subsets. In total, there are 2926 subsets.