You have 5 red shirts, 5 green shirts, 6 pairs of pants, 8 green hats and 8 red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats?
I don't know how you would solve this...
You can have a green hat and a red shirt 8 x 5 combos
or you can have a red hat and a green shirt 8 x 5 combos
each of these combos can have 6 pants to choose from (8 x 5 + 8 x 5) x 6=?