2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4, 5,
6, 7, 8, 9, 10}.
(a) How many of these functions are strictly increasing (i.e.
f(1) < f(2) < f(3) < f(4) < f(5) < f(6))? Hint: How
many different possibilities are there for the range of f? For each
range of f, how many strictly increasing functions are there?
(b) How many of these functions are non-decreasing (i.e. f(1) ≤
f(2) ≤...