The number of functions from an m element set to an n element set is

A. m + n
B. m^n
C. n^m
D. m * n

Question

The number of functions from an m element set to an n element set is

A. m + n
B. m^n
C. n^m
D. m * n

Accepted Answer

n^m A function from a set A (with m elements) to a set B (with n elements) assigns each of the m domain elements exactly one image in B. For each domain element, there are n independent choices, so by the product rule the total is n * n * ... * n (m times) = n^m.

The number of functions from an m element set to an n element set is A. m + n B. m^n C. n^m D. m * n