The game of euchre uses only the 9s, 10s, jacks, queens, kings, and aces from a standard deck of cards

Question

How many five-card hands have at least two red cards?

Answer 1

so we only use 24 cards, of which 12 are red

number of 5-card hands = C(24,5) = 42504

let's exclude number with no reds and only one red
number with no reds = C(12,0) x C(12,5) = 792
number with 1 red = C(12,1) x C(12,4) = 5940

no number with at least two reds
= 42504 - 792 - 5940
= 35772