Number of functions from Karnaugh maps

Givn a function $f(w,x,y,z)=\Sigma(1,4,5,7,13)+\Sigma_\phi(0,8,9,12,15)$
I set up a karnaugh map for it, and my question is:
Other than counting, what is the best way to calculate how many $f$ are there?
I know this is somewhat a combinatorics question, but since the karnaugh map works in a bit change not all combinations are valid functions.

• What are Σ and Σϕ? – user253751 Jan 19 '16 at 8:08
• Sum of products of the minterms and the dont cares of the function. – Yinon Eliraz Jan 19 '16 at 8:09
• I don't know what that is supposed to mean. And if they're functions, why do their parameters have nothing to do with w, x, y or z? – user253751 Jan 19 '16 at 8:16
• en.wikipedia.org/wiki/Karnaugh_map – Yinon Eliraz Jan 19 '16 at 8:20
• I know what a Karnaugh map is. I don't know how Σ(1,4,5,7,13) is "the sum of the products of the minterms" and likewise how Σϕ(0,8,9,12,15) is "the sum of the products of the dont-cares". – user253751 Jan 19 '16 at 8:26

(because $A\overline A$ can be added to anything, ad infinitum, for example)