Valid combinations of a 3 letter alphabet
I was hoping one could tell me how to calculate the following problem in the generic form.
3 possible values A,B,C.
where the following constraint states that, "A" must always exist in a combination.
N is the number of columns in a grid that one of the values will be placed.
if N = 2, then the following are valid combinations:
Invalid combinations are
as these do not have at least one A.
How would you calculate this for N = 3 or N = 4 etc ?
In another example, I can see how the binary alphabet of A,B for N columns can work without the restriction on A.
That is, it is 2^n where n is the number of columns or input number. For example, a 4-input truth table would be 2^4 and 10-input truth table would be 2^10.
However the above scenario has me stumped.