First slide

Permutations

Question

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

Moderate

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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