Question 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.