If X is the number of different characters your password can contain then the total number of possible passwords exactly 8 characters long is X^8. The number o

If X is the number of different characters your password can contain then the total number of possible passwords exactly 8 characters long is X^8. The number of passwords that are less than 8 characters long is X + X^2 + ... + X^7 which is significantly less than X^8 for large X. So your point is even more valid.