# You have created a (random) 5-digit password for your computer. A hacker tries to break in to your computer. What is the probability that he is successful on the first attempt?

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NJ Share
May 15, 2018

$1$ in $100 , 000$

#### Explanation:

Each digit of the password can be one of ten possible digits (0,1,2,3,4,5,6,7,8,9). There are 5 password digits that need to be selected.

The first position has $10$ possible digits.
So does the second.
And the third, fourth, and fifth.

$10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 = {10}^{5} = 100 , 000$

So there are $100 , 000$ total combinations of passwords.

Hence, the odds the hacker guesses is $1$ out of $100 , 000$.

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