Question

A website requires a four-digit numerical password in which the digits cannot repeat. How many possible passwords are there?

24
5,040
151,200
3,628,800

Answer 1

Think of there being 4 slots, each containing one number _ _ _ _

In the first place, there are 10 choices because there are ten digits 0-9
10 _ _ _

In the second place there are still 0-9 digits, but there one of these is taken. So there are 9 options for the second place.
10 9 _ _

Using the same logic, there are 8 options for the third slot, and 7 options for the fourth slot.
10 9 8 7

Multiplying these numbers together gives 5040 possible options.

Answer 2

Another way to do this is to view this scenario as having 10 options and you pick 4.
\[_{10}P_4=\frac{10!}{(10-4)!}=\frac{10!}{6!}=10*9*8*7\]