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How many onto functions are there from a set with three

Question: a. How many onto functions are there from a set with three elements to a set with two elements?

b. How many onto functions are there from a set with three elements to a set with five elements?

c. How many onto functions are there from a set with three elements to a set with three elements?

d. How many onto functions are there from a set with four elements to a set with two elements?

e. How many onto functions are there from a set with four elements to a set with three elements?

f. Let cm,n be the number of onto functions from a set of m elements to a set of n elements, where m ≥ n ≥ 1. Find a formula relating c_m,n to c_m-1,n and c_m-1,n-1.

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