From a standard deck of cards, determine the number of seven-card hands that contain at least...

  

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From a standard deck of cards, determine the number of seven-card hands that contain at least two pairs and at least three different suits. For example, the hand 30 34 54 50 70 is a valid hand. (A three of a kind or four-of-a-kind does not count as a pair.) From a standard deck of cards, determine the number of seven-card hands that contain at least two pairs and at least three different suits. For example, the hand 30 34 54 50 70 is a valid hand. (A three of a kind or four-of-a-kind does not count as a pair.)