Question: (a) Let p, q, r, s be integers with p q and r s. How many distinct functions are there with domain [p..q],

(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 x in the domain?

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