Say we have a computer with which we can try 1 password per second. If we make an 8-character password with:
- numbers (10 options);
- symbols (33 options); and
- mixed-case letters (
26 × 2 = 52 options),
we can construct
(10 + 33 + 52) ^ 8 (to the power of eight) different passwords, such as
b9d:9F?.. Thus it takes that many seconds to try all possibilities if we want to crack it.
Now if we have only lower case letters, 26 options, we can only make
26 ^ 8 different passwords, such as
tpotmykq. To crack these we only need
26 ^ 8 seconds to try all possibilities.
(10 + 33 + 52) ^ 8 = 6634204312890625
(26) ^ 8 = 208827064576
6634204312890625 / 208827064576 = 31769 (close to 30,000)
It depends how many symbols you can make, for example if you count characters like é and ö, then you have a lot more different characters. Usually we count only the printable, 7-bit ASCII set. If space is excluded as symbol, then the resulting difference is 29,190 (closer to 30,000).