How many 8-character passwords can be created from 26 lowercase letters and 10 digits, assuming that in every password there must be as many letters and numbers as?
I'll give it a go:
Reasoning that "as many letters and numbers as" means we need 4 letters and 4 numbers.
So you'll make 4 picks from each category (letters and numbers).
You can duplicate them (i.e., pick each character more than once.)
...so, for your 4 picks from the letters, you'll have
For each of these, you'll have 4 picks from the digits. Similar reasoning, this works out to
This means you'll have
You'll have 8 possible choices for the 1st character, 7 for the second, 6 for the third, etc. This works out to
Best I can do, but I'm far from the ultimate authority for this kind of analysis, so, as always: