Suppose X contains m elements and Y contain n elements. The number of functions from X to Y is

Suppose $X$ contains m elements and $Y$ contain $n$ elements. The number of functions from $X$ to $Y$ is

A
$n m$
B
$n^{m}$
C
$^{n} P_{m}$
D
$^{n} C_{m}$

Solution:

Let $X = \{x_{1}, x_{2}, \dots x_{m}\}$ and $Y = \{y_{1}, y_{2}, \dots y_{n}\}$

For each $x_{1} (1 \leq i \leq m)$ we have n possible images. Therefore, the number of functions from X to Y is $n^{m}$

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