You can put this solution on YOUR website! Pick a card type: 13
Pick 3 of that card type: 4C3 = 4
Pick another card type: 12
Pick 2 of that card type: 4C2 = 6
Total number of ways = 13*12*24 = 3744
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total number of 5-card hands: 52C5
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P(getting Full House hand) = 3744/52C5 = 0.00144
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Cheers,
Stan H.