I have been thinking on combination locks recently, and would like some help with this particular problem.
Problem:
I have a lock with digits 1-9, and the length of the combination is 4 digits. You cannot press the digits 1-9 more than once, and the combination does not have to be typed in any particular order.
Questions:
- Is it true, then, that the possible amount of combinations is 3,024, because 9*8*7*6=3,024?
- Is it also true that 24 of the combinations are correct, since you do not have to type the combination in any particular order? Therefore 1*2*3*4=24.
- Is it true that the chances of guessing it right are 1 in 125 since 3,000/24=125?
Addendum questions:
- If you would change the lock to have a 5 digit combination, would the chance to guess it right be the same as if it were a 4 digit combination? Since the possible combination amount is 15,120 (9*8*7*6*5), the amount of right combinations is 120 (1*2*3*4*5), therefore 15,000/120=125. The same amount of chance as if it were a 4-digit combination?
- If all this is true, then wouldn't a 6-digit combination actually be less secure? I.e., you have a greater chance of guessing the right combination? (1 in 84, if I am doing it right.)
Help is greatly appreciated. I have not done probability in a long time and am wondering if I am even doing it right.
Thanks, guys.
Fatal Sylence
Hmm, okay. Can you direct me towards a resource that explains the "n things taken r at a time"?
Also, were my other questions correct?
Finally, would a 5 digit combination be more secure? A 4 digit combination has the same chance to guess right as a a 5-digit combination, but don't you have a greater chance to guess it wrongwith 5-digits?
Look at this page.
Also look at this page. You change those numbers and hit .
OH!!! Gosh! I get it! It does not matter how many ways you can arrange a set of four since order does not matter. I understand. One of these 126 sets encompasses all the ways you can arrange it since order does not matter.
So, if the person was good at math, they would realize that since order does not matter, there are only 126 possible combinations. Wow, I get it. Thank you.
EDIT: Is there a formula or calculator that can display all the possible sets for a 1-9, 4 digit combination? Or any other numbers for that matter?