For Inyo permits, you must have an exit permit for Whitney to be able to exit via WP, in addition to your entry permit. The exit permits are very difficult to get since there aren't many of them. That's why lots of people exit via Cottonwood Pass. You do not need an exit permit for entry permits issued by the other agencies such as Yosemite, SEKI or Sierra National Forest, though you do have to select Whitney as you exit.?