How many possible combinations in $7$ character password? The password must be $7$ characters long and it can include the combination: $10$ digits $(0-9)$ and uppercase letters $(26)$.
My Solution:
Thus in total there are $7$ slots, each slot could be either $0-9$ or $26$ letters $= 36$ possibilities for each slot, therefore, $36^7$ would be the number of password combinations? 
Am I correct?

Your solution is correct. You can also look at this as a function from a set with $7$ elements to a set with $36$ elements.
How many functions are there from a $7$ element set to a $36$ element set?
For each element in the domain, how many elements in the codomain can it possibly get mapped to? $36$
Since there are $7$ elements in the domain, there are a total of
$$36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36=36^7$$
possible functions.
