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: Howmany different possibilities are there for the range of f? For eachrange of f, how many strictly increasing functions are there?
(b) How many of these functions are non-decreasing (i.e. f(1) ?f(2) ? f(3) ? f(4) ? f(5) ? f(6))? Hint: What are the yards? Whatare the trees? Or, if you prefer, what are the stars and what arethe bars?
