There should be a way to get a starting wand (and other starting weapons) in the event that you accidentally sell the only one you can equip. As it is, I can buy a Level 19 wand, but I can't equip it. The mercenaries' merchants will not sell to me, so I cannot see if they would carry a wand I need.
@Dubster
Are you counting Deck ABC as different from Deck BCA? Can someone choose not to equip an item? If so, then pretend "no item" is the same as an item, and you've got 12 items.
Anyway, You have 20 cards, and 3 spaces, so the choose function 20 choose 3 =20!/(17!*3!)=20*19*18/6=20*19*3=1140
Each of those 1140 character combinations can then gets an item per character. A can equip items 1,2,3...11. One character equips 1 item in 11 ways, 2 characters equip 2 items in 11^2, and 3 in 11^3.
So 1140*11^3=1,517,340, which is a factor of 6 lower than your answer, because you didn't properly apply the binomial.
@wowhead....
"the random chances also seem to be broken for me... like missing 5 out of 7 50% poisons"
That happens with probability given by (1/2^7)*(7!/(5!*2!))=1/128*21~19%.
So you should expect that outcome rather frequently.
 "Kongai"){kind=icon}
 "Hands of War"){kind=icon}