(a) Let p, q, r, s be integers with p ≤ q and r ≤ s. How many distinct

functions are there with domain [p..q], and codomain [r..s]?

(b) Let P and q be integers with p ≤ q. How many distinct functions

are there of the form f: [p..q] → [p..q] such that f(x) < x for all r

in the domain?