A password consists of eight characters. Count the number of possible passwords

Question

A password consists of eight characters. Count the number of possible passwords that can be created in each of the following scenarios. You may assume numbers refer to digits “0” through “9” and letters refer to “a” through “z” (lower case only). Characters other than letters or numbers are not allowed. (a) The password can contain only letters. (b) Repeat Part (a) if all of the letters must be different. (c) Passwords must contain exactly two numbers (in any location). (d) Repeat Part (d) if the sum of the two numbers must be even. (e) At most one letter can appear in the first five characters of the password. [HINT: In some cases, it may be easier to decompose the set of passwords into several mutually-exclusive types that can be more easily counted, and then add the number of passwords of each type to find your answer.]

Explanation / Answer

A) If password contains only letters,we have 26 letters. And if repitition of letters is allowed, then number of permutations will be 26^8 . As it is 8 letter password and any alphabet can come in any place.

B) If letters must bhi different, i.e repitition is not allowed,then 26*25*24*23*22*21*20*19 will be possible password.

C) 2 numbers:- we have in total 10 numbers starting from 0 to 9.

Exactly 2 numbers = 10*9 permutations (if they are different numbers)

D) sum must be even = 9*5 (as we have in total 5 even numbers 0,2,4,6,8)

As per chegg guidelines, solved first 4 parts. Feel free to ask doubts in it

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