Let A be a set of 10 elements and B be a set of 15 elements

Let A be a set of 10 elements and B be a set of 15 elements. How many functions can be defined with the domain of A and the co-domain of B?

Solution

In the function we need to match every element in set A to a element in set B. For each element in set A, there are 15 possibilities in set B, so in total there are (15)^10 possibilities for all the 10 elements in set A. Each possibility represents a distinct function that can be formed.