1. Let n ≥ 1 and m ≥ n be integers. Consider the set G of functions g : {1, 2, . . . n} → {1, 2, . . . , m}. How many functions are in G? How many one-to-one functions are there in G? How many...

1. Let n ≥ 1 and m ≥ n be integers. Consider the set G of functions g : {1, 2, . . . n} → {1, 2, . . . , m}. How many functions are in G? How many one-to-one functions are there in G? How many bijections?

2. Show that the number of bijections f : A → B is equal to the number of bijections g : B → A. (Hint: define a bijection between {bijections f : A → B} and {bijections g : B → A}, and use the bijection case of the mapping rule!)