I got an additional task from my math teacher today: Theres a card with 12 fields, but only 6 of them are filled with a symbol. In every card, there are 3 star symbols, 2 moon symbols and 1 sun symbol:
The task is to calculate how many different cards of this kind can exist/maximal amount of different cards.
My Solution was $12! - 6!$, because I thought that if I would take one star, I would have 12 places to place and if I would take another one, I would have 11 places to place.
But I already found out that this isnt the right solution, because the places of one of the symbols are interchangeable without making the card look different.
So can someone give me a hint to the right solution?
Any help will be greatly appreciated.