Question

Suppose that you have a very simple 4-digit code for a bicycle lock (digits 0 through 5 allowed), where no digit may be used more than once in the code. what is the probability that someone could randomly guess your code correctly in just a single try?

Answer 1

Answer: Approximately 0.3% (see details below)

Explanation:

I am assuming that the order of the digits matters, for example, 4102 is considered a different code from 2014.

Since a digit can't be repeated this becomes the number of permutations of 4 elements drawn from a set of 6 (digits 0 through 5) without replacement. The number of possibilities is 6 (first digit) times 5 (second digit guess) times 4 and so on until 4 digits have been selected:

`P=(1)/(6\cdot5\cdot4\cdot3)=(1)/(360)\approx 0.3\%`