Question

1) Assume that a password can contain upper and lower-case letters (26), digits, and special characters from the set { !, #, $, %, &, * }. Furthermore, each password must start with a letter and must contain at least one digit and one special character. How many different six-character passwords can be formed according to this specification?

Answer 1

there is total (26+26 = 52) upper and lower case letters

total digits= 0 to 9 =10

total characters = 6

We have 6 positions. Each of those positions can be occupied by any of
the (52+10+6) = 68 choices available

total combination possible = (52+10+6)^6 = 68^6

the passwords with NO digits and no special characters are = (52)^6

Total passwords with atleast a digit and a specia character = 68^6 - 52^6

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Total number of passwords possible with atleast one character and atleast
one digit = 68^6 - 52^6 = 79096872960