Combinatorics inclusion exclusion

183. () (onto functions and Stirling numbers of the second kind) (a) Given a function f from the k-element set K to the n-element set [n], we say f is in the set A, if f(z) i for every x E K. How many of these sets does an onto function belong to? What is the number of functions from a k-element set onto an n-element set? (b) Find a formula for the Stirling number (of the second kind) S(k, n)