AIME 2009a Problem 9

A game show offers a contestant three prizes A, B and C, each of which is worth a whole number of dollars from $\$ 1$ to $\$ 9999$ inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular day, the digits given were $1, 1, 1, 1, 3, 3, 3$. Find the total number of possible guesses for all three prizes consistent with the hint.