I have been thinking on combination locks recently, and would like some help with this particular 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.
- 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?
- 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.