Each dye box contains 7 random dyes (5 common and 2 uncommon or rare).
Dyes can be unlocked for unlimited uses to color armor on all characters. Dye bottles can also be recycled in the mystic forge.
— In-game description
There are 382 possible colors that can drop from a Dye Pack including 181 Common, 119 Uncommon, and 82 Rare.