Question 4: [adapted from Problem 2-56 of the textbook] A computer system uses p

Question

Question 4: [adapted from Problem 2-56 of the textbook] A computer system uses passwords that contain exactly eight characters, and each character is 1 of the 26 lowercase letters (a-z) or 26 uppercase letters (A-Z) or 10 integers (0-9). Let denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the number of passwords in cach of the following events: (a) S2 (b) A (c) A' B, where notation A, denotes the complement of event A . d) Passwords that contain at least integer (e) Passwords that contain exactly 1 integer

Explanation / Answer

a) There are 26+26+10 = 62 options for a character

Number of passwords possible = 628

= 2.18x1014

b) Number of passwords with only letters = 528

= 5.346x1013

c) Number of passwors such that it is not only letters or only intigers

= 628 - 528 - 108

= 1.65x1014

d) Number of passwords with at least 1 intiger = 628 - 528

= 1.6488x1014

e) Number of passwords that contain exactly 1 intiger = Number of positions intiger can assume x Number of intigers x Number of options for other 7 positions

= 8 x 10 x 527

= 8.2246x1013

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