Drawing cards

Suppose I draw three cards from a deck. How many ways can I draw two red cards and then a face card?

For this questions I got:

I got these numbers by looking at the number of cards that could be chosen on each draw. If you are picking your first card and want a red card: you have 26 choices. If you also want your second card to be red, there would be 25 red cards left. If you wanted your last card to be a face card, then there would be 12 cards.

But the only thing I wasn’t sure about is accounting for the red face cards that could be chosen on the first two draws. Not sure if someone else found a different way to solve.

@ksimmon1 What if one or two of your red cards also happens to be a face card?

Would we add up all the difference scenarios?

Scenario 1:
Draw Red Card No Face
Draw Red Card No Face
Draw Face Card

Scenario 2:
Draw Red Face Card
Draw Red Card No Face
Draw Face Card

Scenario 3:
Draw Red Card No Face
Draw Red Face Card
Draw Face Card

Scenario 4:
Draw Red Face Card
Draw Red Face Card
Draw Face Card

This would make our answer: