"There is a simple programming language known as TRIVIAL. In this language only the following 6 types of instructions are allowed:

a.) Input X, a natural number

b.) Go to step # -

c.) Set X := X + 1

d.) If X = 0, then go to step # -

e.) If > 0, then set X := X - 1

f.) Stop.

Suppose that a program must begin with the instruction Input X and end with the instruction Stop. How many different programs are there, written in the language TRIVIAL if the program is n steps long?"

Similar to the first, the next is: "Suppose that a TRIVIAL program can begin with one or more statements Input X, where X may be any letter of the alphabet; for example, we may begin with Input A and then following with Input B. Then we allow statements of the form A := A + 1, and if B > 0, then set B := B - 1, and so on, provided that A and B are input variables. If the program begins by reading in two variables A and B, then how many different trivial programs are there using n steps?"

In this one, need to take into account 26 letters and im assuming combinatorics.

Thanks for your help.

Under ordinary situations, it would just be 6! I am assuming?