Question

A password consists of 4 letters among 26 lower-case English alphabet letters and 10 digits: 0,1,...,9. (i) How many different passwords that contain at least one digit can be formed? (ii) How many different passwords that contain at least one digit and at least one letter can be formed?

Answer 1

i) of 0 possible When there is restrictions, the number choices for each of the 4 letters the password (26+10 f o = 36. When there is restrictions, the total number of possible O

passwords 36 x 36 x 36 x 36 4. = (36) do passwords If the passwords not contain any digit lie. the contain I only letters), then the possible number of for choices each A letrens of the of the password 26.

asswords . If do the pas di not contain any then the total number of possible pas swords - 26 x 26 x 26 x 26 1 (26) of passwords number at least : The that contain digit one 4 4 (36) (26) 1679616 - 456976 = 1 2 2 2 640

li> If the do pass sswords not contain any letter lie. the contain digits) then the number of possible choices for each of the letters of passwords only di 4 the password 10. the nor passwords do contain any letter, total possible passwords number then of 10 X 10 X 10 X 10 1 4 c 110)

of number passwords :: The contain at least that and at least one digit Lether one 4 = (360° - { (26)² + (10)} 1679616-{ 456976 + 10000 n] 1212640