Solution: 2016 Fall Final - 1
Author: Michiel SmidQuestion
Consider a set $A$ having size 7 and a set $B$ having size 9. How many functions $f : A \rightarrow B$
are there?
(a)
$7!$
(b)
$9!$
(c)
$9^7$
(d)
$7^9$
Solution
Well, they aren’t one-to-one functions, so each input has 7 possible outputs
The first input has 9 possible outputs
The second input has 9 possible outputs
…
The seventh input has 9 possible outputs
$ 9^7 $