# Elijah forgot his pass code for a certain website. He knows it is made up of 5 digits and no digit can be repeated. If he randomly chooses 5 different digits, what is the probability that he chooses his pass code?

Feb 20, 2017

The chances are $\frac{1}{30 , 240}$.

#### Explanation:

Use the permutation formula, as order matters, to determine the number of permutations that are possible. Call the number of permutations $P$. There are 10 possible digits to choose from, and he needs to choose $5$ different digits, so $P$ is given by

P = (n!)/((n - r)!)

P = (10!)/((10 - 5)!)

$P = 30240$

If he randomly chooses one set of $5$ digits, than his chances that he chooses the correct pass code is $\frac{1}{30 , 240}$

Hopefully this helps!