Is this a good enough proof?

Question

Is this proof good enough? If not, any feedback would be appreciated. Thanks.

Either exhibit $333 $ different boolean functions on the three variables $p; q; r,$ or prove that there aren’t $333$ different such functions.

Proof: Using the formula $2^{2^n}$ for calculating the total number of functions any boolean function can have, the total number of functions the variables $p,q,r$ have is 256.Therefore there aren't $333 $ different boolean function in the variable $p,q,r.$

Answer 1

As pointed out in the comments:

1. You may want to explain what $n$ is in your proof
2. Otherwise, your proof is fine--assuming that the formula $2^{2^n}$ has already been proven elsewhere.

Converting comments to answer to get off "unanswered" queue