TITLE: A question about "ways" in Math
QUESTION [1 upvotes]: How many ways are there to make a two-character alphanumeric password, but it must include an integer?

The solution is:
$36^2-26^2$.
However, why can't it be:
$36×10$? Since one 'slot' is a forfeit for the integer.

REPLY [0 votes]: 36x10 would mean that the second character was always a number. This misses out 10x26 cases.
The solution is to take the number of cases with two alphanumeric characters (36x36) and subtract all those cases that don’t have at least one number - ie both letters (26x26). So $36*36-26*26 = 620$ and you get the same answer with $36*10 +10*26 =620$
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