Is it permissible to buy a driver's license, knowing that one has not learned to drive due to [the issue of] intermingling [with men], and is this permissible for a married woman whose husband does not wish for her to intermingle [with men], yet she needs the license?

The basic principle is that a Muslim should abide by laws that do not contradict Islamic law (Sharia (definition)) and that benefit people. Purchasing a driver's license without an examination violates the law, endangers people's lives, and involves deception and bribery. Therefore, it is not permissible to purchase it. Furthermore, the fundamental principle for a woman is to remain in her home, as Allah Almighty says: "And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger."