Consider a symbol vocabulary that contains $c$ constant symbols, $p_k$ predicate symbols of each arity $k$, and $f_n$ function symbols of each arity $k$, where $1\le k \le A$. Let the domain size be fixed at $D$. For any given interpretation-model combination, each predicate or function symbol is mapped onto a relation or function, respectively, of the same arity. You may assume that the functions in the model allow some input tuples to have no value for the function(i.e., the value is the invisible object). Derive a formula for the no. of possible interpretation-model combinations for a domain with $D$ elements. Don't worry about elimination redundant combinations.
I've understood the first half of the question, that there are $k$ predicate symbols $(p_1,p_2, \dots, p_k)$ and there are also $k$ function symbols $(f_1,f_2, \dots, f_k)$.
What is it meant by
interpretation-model combinations for a domain? And how do I derive a formula for the no. of possible interpretation-model combinations for a domain with $D$ elements?