Since there are only 9 different major numbers, this is a very simple situation. There are several ways to deal with this.
It should be understood that the description can be extracted from tblMajor and should never need to be input by the user.
The easiest, and very likely the best solution, would be to display both the MajorNo and Description together in the MagorNo dropdown. To do this you merely need to concatenate the values as you retreive them from the database or as you add them as options in the dropdown.
An overkill approach would be to do this with Ajax. With only 9 major numbers to deal with, it is easy enough to simply pass the data along with each response. If you had thousands of items to deal with, you would probably want to use an Ajax solution.