Find the number of functions from a set A with m elements to a set B with n elements.

Explanation

Let `A={a_(1), a_(2),…….a_(m)} and B={b_(1), b_(2),……b_(n)}`.
First, to define the image of `a_(1)` we have n choices (any element of B). Then to define the image of `a_(2)` we again have n choices (since `a_(1), a_(2)` can have the same image). Thus we have n choices for the image of each of the m elements of the set A. Therefore, the number of different ways of defining the images of elements of A (with images in B) is `n xx n xx ....x n` ( m times) `=n^(m)`.