What is the combination probability?

[Lysander]

We have digilocks at work with buttons which say 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, X, Y, Z.

Format of codes is normally <number><number><number><number><letter>

Now, the order of the numbers + letter doesn't matter. You will find this with many non-electrical digilocks.

What probably is there that someone can gain entry after just hitting four random numbers and one random letter in any order?

 

[Lysander]

The probability will be 1/(10*9*8*7*3)=6.6x10-5
Assuming numbers can only be used once, otherwise it would be about half that

I am sorry, I am bad at maths. Does this mean 61% chance of success? If we were to represent this as a percentage?

 

[Lysander]

0.000066% (i think)

Got to be more than that, surely.

 

[Lysander]

Yep, though I missed the bit about the order not mattering. See the edited post, about 0.1%

Is that all? Wow, I was assuming it was much higher than that.

 

[Lysander]

There are 210 combinations of 4 numbers, and 3 letters to choose, so 630 possible combinations

The order of numbers and letters doesn't matter.

So 1234Y will gain you entry just as 14Y23 will.

If we don't think of them as letter + numbers but just five characters, surely the chance will increase?

 

[Lysander]

If each button is only used once and there are 13 labelled buttons, with five buttons in the code and the order doesn't matter, isn't the odds simply 5/13?

Yes indeed, I was looking more for something like this. So around 38% chance of success with one go.

 

[Lysander]

Try these first

1234A
1111A
9999A

@frying_pan_cat @UTmaniac

You can't reuse a character.

 

[Lysander]

Nah, you had it in the first line! The order doesn't matter, we know there are 4 digits and 1 letter required in any order, ergo you also don't need to look at the possibilities of pressing more than one letter etc...

What is the correct answer then? I'm confused.

Five characters [four numbers + one letter], any order, no repetitions.

 

[Lysander]

Digilocks are ornamental, on most of them you can simply shine a light at the right angle and see which buttons were pressed due to the marks left by fingers. Add to this the fact that the sequence is irrelevant and they're pointless.

I think saying they're pointless is a bit much. That is what this thread has tried to determine.

@dowie thinks that you have a 0.16% chance of success to gain entry without knowing the code, in spite of no number repetitions and an irrelevant character order. That's hardly pointless.