Let’s count. Occupancy problems with sequences

Do your best in trying to solve the following problem. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

(bullet) To multiply polynomials, you can use the following widget:

https://www.wolframalpha.com/input/?i=Expand

Exercise. Calculate the number of possible codes of 10 digits that use only the digits 1, 2, and 3, and in which 1 appears at least 4 times but not more than 7 times, while 3 appears an even number of times.