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  • 4 years ago

Please help! This is a Combinations problem. In a standard deck of cards, how many 4-card hands are there that contain at most 1 heart? I keep getting 118,807 but the real answer is suppose to be 201, 058. I always get confused with card questions. Can you help me?

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  1. rivermaker
    • 4 years ago
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    You can choose one heart in 13 ways and for each of these you can choose 3 non-hearts in \[^{39}C_{3}\] ways. You can choose 4 non-hearts in \[^{39}C_{4}\]. So the answer is \[13 * ^{39}C_{3} + ^{39}C_{4}\]

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