3. Suppose that a password for a computer system must have exactly 8 characters.

Question

3. Suppose that a password for a computer system must have exactly 8 characters.
a. how many passwords are possible that only use lower-case alphabetic characters.
b. how many passwords are possible that can use either upper and lower case characters.
c. how many passwords are possible that use a combination of upper and lower case character as well as exactly one numeric digit in the last position.
d. how many passwords are possible that use a combination of upper and lower case characters as well as exactly one numeric digit if the position of the numeric digit is variable.

Explanation / Answer

we have lower case characters 26    upper case characters 26

a) only with lower case characterers   u can chose any character out of 26 thus

total number: 26 * 26 * 26 * 26 * 26*26*26*26 = 208827064576 possible combinations.

b) upper + lower = total we have 52 characters .

total number = 52*52*52*52*52*52*52*52 = 53459728531456 possible combinations.

c) one fixed digit at last postion thus

possible combinaitons = 52*52*52*52*52*52*52 *1 = 1028071702528 possible

d) if last digit is variable u have 1 digit to choose out of 10 digits.

52*52*52*52*52*52*52 *10 = 10280717025280 possible combinations.

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