Math Question Need help!!?

Question

From a deck of 52 cards, the 12 face cards are removed. From these face cards, 4 are chosen. How many combinations that have at least two red cards are possible?

Explain please.

Answer is 360 combinations

Answer 1

so there are only 12 face cards we're concerning about.
there are 6 face cards that are red.

find the combination of 2 Red and two others.
(6*5)/2 * (6*5)/2 = 30

find the combination of 3 Red and another face card.
(6*5*4) / 3! * 6 = 120

find the combination of 4 reds
(6*5*4*3) / 4! = 15

so the total would be 30 + 120 + 15 = 165 combinations

oops! my bad! i calculated it wrong. Notices that (6*5)/2 * (6*5)/2 = 225 ways (not 30)

225 + 15 + 120 = 360

Answer 2

NOT SURE, but here is my attempt:
Since they are all face cards, we only care about color. We have 6 red and we have 6 black.. each 50% chance of being selected.
it is easiest to think of it as we need two red cards and the other two cards can be anything.
6 reds * 5 reds * any 10 * any 9
6*5*10*9 = 2700 possible??

Answer 3

You're choosing 4 out of 12 [this is much like Keno, by the way, except they use 80 numbered balls]. 6 of the 12 are red, 6 not. so multiply choices for red times choices for black:

2 red: 6C2 • 6C2 = 15•15 = 225
3 red: 6C3 • 6C1 = 20•6 = 120
4 red: 6C4 • 6C0 = 20•1 = 20
total: 365 ways.