Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: PigeonHole Help

  1. Mar 22, 2010 #1
    PigeonHole Help!!

    1. The problem statement, all variables and given/known data

    A computer password is formed from 4, 5 or 6 characters. A character is either a lowercase or uppercase vowel: (a, e, i, o, u, y) or (A, E, I, O, U, Y) (passwords are case sensitive) or else it is a digit from the set {0, 3, 4, 7, 9}. Each password must contain at least one digit. How many passwords are possible?

    2. Relevant equations

    Product or sum rules

    3. The attempt at a solution

    12 letters, 5 digits

    if 4: 3 letters and 1 digit.
    So 3*12= 36 letters possibilities
    1*5= 5 digit possibilities

    36+5= 41 passwords




    I'm not sure if this is how????
     
  2. jcsd
  3. Mar 22, 2010 #2

    Mark44

    Staff: Mentor

    Re: PigeonHole Help!!

    This is definitely not how.

    Count the numbers of 4-character, 5-character, and 6-character passwords separately. For 4-char passwords, look at separate cases for 1 digit, 2 digits, 3 digits, and 4 digits.
    4-character pwds
    1 digit + 3 characters: 5 * 12 * 12 * 12 = 8640 possible choices.
    2 digits + 2 chars ...
    3 digits + 1 char...
    4 digits + 0 chars ...

    5-character pwds
    1 digit + 4 characters:
    2 digits + 3 chars ...
    3 digits + 2 chars ...
    4 digits + 1 char ...
    5 digits + 0 char ...

    Do the same for 6-character passwords. Add up all the possibilities.
     
  4. Mar 28, 2010 #3
    Re: PigeonHole Help!!

    Suggestion:
    (1) Count all the passwords, ignoring the constraint that they must contain at least one digit.
    (2) Then count all the passwords that do not contain any digits.
    (3) Subtract (2) from (1) to find the number of passwords that contain at least one digit.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook