Solution: 2016 Fall Final - 2
Author: Michiel SmidQuestion
Consider a set $A$ having size 7 and a set $B$ having size 9. How many one-to-one functions
$f : A \rightarrow B$ are there?
(a)
$\frac{9!}{3}$
(b)
$\frac{9!}{2}$
(c)
$\frac{7!}{2}$
(d)
$\frac{7!}{3}$
Solution
The first input has 9 possible outputs
The second input has 8 possible outputs
…
The seventh input has 3 possible outputs
$ 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 $
$ \frac{9!}{2!} $