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A set of poker has 32 cards. 30 of them are in red, yellow and blue,...

A set of poker has 32 cards. 30 of them are in red, yellow and blue, with 10 cards in each colour, given the numbers 1, 2, …, 10 respectively. 2 of them are different jokers, both with the number 0. A card with the number k counts for 2k points. Call a group of cards a ‘good group’ if the sum of their points is 2004. Calculate the number of ‘good groups’ using generating functions.

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