From a standard deck of 52 cards, 5 cards are dealt and the order of the cards is unimportant. In how may ways can you receive at least one face card?
I understand that the answer is 1,940,952 ways which can be calculated by doing $52\choose5$ - $40\choose5$.
My question is why doesn't $12\choose1$ $51\choose4$ also work? I'm trying to choose a face card and then choose the four other cards from the rest of the deck, but it equals 2998800.