A deck of cards has 4 suits: diamonds, hearts, clubs, and spades. The suits of diamonds and hearts are both red and the suits of clubs and spades are both black. Each suit has the following denominations: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. The Jacks, Queens and Kings are also called face cards.
Question: In how many ways 2 cards can be drawn such that one card is from red face cards and the other is a black card.
I know this is a combination problem, and I have tried solving it by taking (26!/1!(26-1)!) * (26!/1!(26-1)!). My main concern is whether or not I have to account for whether 2 black cards can be drawn with 0 red cards or 0 black cards drawn with 2 red cards. Thank you for any advice.