Let S and T be finite sets with n and m elements, respectively. (a) How many functions f : S → T can be defined? (b) If m ≥ n, how many injective (one-to-one) functions f : S → T can be defined? (c)...

(a) How many functions f : S → T can be defined?

(b) If m ≥ n, how many injective (one-to-one) functions f : S → T can be defined?

(c) If m = n, how many surjective (onto) functions f : S → T can be defined?