2009 AIME I 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 \text{\$}1 to \text{\$}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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.