N(X)=p and n(Y)=q then the no of function from X-> Y is q^p , how do u prove this

Suppose X = {x_1, ..., x_p}. A function f : X ---> Y is completely determined by its images f(x_1), ..., f(x_p). There are q choices for each image f(x_i) since n(Y) = q. Hence, there must be p * p * ... * p (q times) = p^q choices to form a function from X to Y.

Da fuq.. I can't even do division.