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

I NEED THE ANSWER TO PART E ONLY

Explanation / Answer

e) number of ways no letter in first five charecters =N(for each of first 5 chareter there are 10 choices of digits and for last 3 digits we have 36 choices including letter) =105 *363

number of ways one letter in first five charecters=N(choosing one letter out of 26 and than one place out of 5 for letter) and than put 4 digits in rest of 4 places and then 36 choices for each last 3 charecters

=26*5*104*363

total number of ways =105 *363+26*5*104*363 =65318400000

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