Free: Contests & Raffles.
You can hunt both seasons using the equipment (and during the dates) for which the permit is valid. You can only harvest a total of one elk so if you tag a bull you're done hunting. If you don't tag a bull you can take up your muzzy and go shoot a cow.
You're right but he has an archery bull tag and a muzzy cow tag. If he can't fill either of those permit tags before the modern firearm season maybe he should stay home and watch football??? Just kidding. Shoot a big bull with the archery tag so you don't have to worry about the cow tag or the sea of orange you will face in the modern season. Good luck.
Basically, you can hunt all seasons(rifle, muzzy, and archery) but you can harvest only one elk (either a bull or a cow) and then you are done with your elk tag. Happy hunting