Frank C. answered • 01/05/18
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We have five empty spaces _ _ _ _ _ , representing not just the characters for any possible password, but also the five numbers we'll multiply together to calculate all the possible permutations (*We are calling them permutations because order matters whenever making a password). Because we're just creating passwords and it doesn't say otherwise, let's assume that we're allowed to repeat characters. Now we're ready to consider the amounts of possibilities for each character:
- The password must start with a letter so there are only 4 possibilities
- Let's say that this is letter #2, there are 4 possibilities again, since we can repeat
- Let's say that this is digit #1, there are 6 possibilities
- Let's say that this is digit #2, there are 6 possibilities again
- Let's say that this is digit #3, there are 6 possibilities again
4×4×6×6×6 = 3,456 possibilities within this letter/number permutation.
Notice now that this is only one configuration of letters & numbers, and since we want to say that "AA111" is a different password from "A1A11," we have to multiply this number by all the possible permutations. This is where it matters that the password must start with a letter. It is now much easier to count the permutations by hand:
AA111
A1A11
A11A1
A111A
These examples show us that there are only 4 permutations we can use. If you wanted to use the formula for this, nPk = n!/(n-k)!, just remember that because the first character is locked in, we can leave that out of the process. So our full set is actually n = 5-1 = 4, and let's use the number of letters as the selected set to get k = 2-1 = 1.
4P1 = 4!/(4-1)!
= 4!/3!
= (4×3×2×1)/(3×2×1) = 4
So to get our total, we will multiply 3,456×4 = 13,824 total permutations
Have a good weekend!
