CGMO 2004 Problem 4

A deck of $32$ cards has $2$ different jokers each of which is numbered $0$ . There are $10$ red cards numbered $1$ through $10$ and similarly for blue and green cards. One chooses a number of cards from the deck. If a card in hand is numbered $k$ , then the value of the card is $2^k$ , and the value of the hand is sum of the values of the cards in hand. Determine the number of hands having the value $2004$ .