The randomness favors having different classes.
If a boss has 5 drops, one for each class you have and they all have a 20% chance of dropping and always drops one, it would take an average of 11.41666~ runs to get the drop for all of your characters.
If you ran the same boss with 5x one of the classes it would take an average of 25 runs to get the drop on all of your characters.
When you include multiple bosses it gets better for different classes.

Try to have classes that work well together without much thought. You can set up a sheep macro prior to fighting easily enough, but doing it mid-fight doesn't work well. Things that are automatic or fire and forget, like buffs, are good, but utility that requires attention, like chain trapping with a hunter, is going to use more attention than it's worth. Have a plan to set all of your dps macros on the same button and mash that button. You could have them all on different buttons and mash them all for more control, but plan around them all being mashed. If you can't properly set someone up on a castsequence macro(or just a /cast if it's one spell), then they are probably not contributing as much as you'd like.