permutation and combination

The game of euchre uses only the 9s, 10s, jacks, queens, kings, and aces from a standard deck of cards
How many five-card hands have at least two red cards?

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  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

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