A Combinatorics III Problem by Pr. Fares Salem
Probability
Level
1
Unfortunately you can’t remember the code for your four-digit lock. You only know that you didn’t use any digit more than once. How many different ways do you have to try?
The answer is 5040.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
There are 10 digits (0, 1, …, 9) and each one appears at most once. The number of orderings of these digits is 10P4 = 5040. It would take a very long time to test that many combinations, so 4-digit locks are very safe.