How many combinations are there in a 7 character password?

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The password must be $7$ characters long and it can include the combination: $10$ digits $(0-9)$ and uppercase letters $(26)$.

My Solution:

Thus in total there are $7$ slots, each slot could be either $0-9$ or $26$ letters $= 36$ possibilities for each slot, therefore, $36^7$ would be the number of password combinations?

Am I correct?

user46372819

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asked Feb 16, 2016 at 6:12

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1

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You are correct. $36^7$ is the right answer.

answered Feb 16, 2016 at 6:47

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Your solution is correct. You can also look at this as a function from a set with $7$ elements to a set with $36$ elements.

How many functions are there from a $7$ element set to a $36$ element set?

For each element in the domain, how many elements in the codomain can it possibly get mapped to? $36$

Since there are $7$ elements in the domain, there are a total of $$36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36=36^7$$ possible functions.

answered Feb 16, 2016 at 6:50

user46372819user46372819

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Calculate Passwords

[Slides] We can calculate the total number of passwords possible by analysing the number of characters used. The calculation uses a calculation speed based on the number of passwords tried with brute force:

Theory

The strength of a password relates to three major elements:

• The number of characters in the password. The more characters that are in the password the stronger the password will be.
• The range of characters in the password. The wider the range of characters in a password will increase its strength, especially to use non-alphabet ones (such as "!", "@", and so on).
• The cracking speed of a brute force generator. This relates to the speed of the cracker, such as 1,000,000 tries per second.

For example if we have lowercase letters [a-z] we have 26 characters, and add uppercase letters [A-Z], we get 52 characters. If we then have 5 characters in the password, the number of password combinations will be:

aaaaa to ZZZZZ

which will be 52 to the power of 5 = 380,204,032

If we crack these passwords at a rate of one million per second then it will take 380 seconds to try all of them (6.23 mins).

Here is the calcuation for [a-zA-Z] with one million password attempts per second. We can see that for seven digit password it takes 11.9 days, and for a 10-digit one it takes over 4,000 years:

But if we now use 1 billion passwords per second, we can see that a seven character password only takes 17.13 mins to crack:

In general terms, we can calculate the number of passwords for a 5-character password with a range of character sets:

Presentation

How many passwords can you make with 7 characters?

How many combinations are in 7 digits?

How many possible combinations are there for a password?

How many 10 character passwords are possible?