I have a number that is a string of 1s, followed by a string of 2s, followed by a string of 3s. For example 111233. There must be at least one of each digit.

Similarly I have a second number that is a string of 3s, followed by a string of 2s then a string of 1s, with again at least one of each of the different digits. For example 332211111.

Adding these two numbers together I get the answer 44443444.

How many different possibilities are there for my two numbers?