Results 1 to 3 of 3

Math Help - Permutations and Combinations problem

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Permutations and Combinations problem

    This one has really been troubling me. The question is:

    A computer program requires a password of at least 6 but no more than 8 characters. All letters (of the English alphabet, not case sensitive) and digits (0 to 9) may be used. The password must contain at least one digit and one letter. How many different passwords are possible?

    I used the indirect method for each case and got down to:

    Case 1: 6 character password

    36^6 - (26^6 + 10^6)

    Case 2: 7 character password

    36^7 - (26^7 + 10^7)

    Case 3: 8 character password

    36^8 - (26^8 + 10^8)

    And then I added all the cases together. Is that correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello dancecubed

    Welcome to Math Help Forum!
    Quote Originally Posted by dancecubed View Post
    This one has really been troubling me. The question is:

    A computer program requires a password of at least 6 but no more than 8 characters. All letters (of the English alphabet, not case sensitive) and digits (0 to 9) may be used. The password must contain at least one digit and one letter. How many different passwords are possible?

    I used the indirect method for each case and got down to:

    Case 1: 6 character password

    36^6 - (26^6 + 10^6)

    Case 2: 7 character password

    36^7 - (26^7 + 10^7)

    Case 3: 8 character password

    36^8 - (26^8 + 10^8)

    And then I added all the cases together. Is that correct?
    I think it is quite correct. For instance:

    In Case 1 (6-character passwords):
    There are 36^6 passwords altogether if there is no restriction, since there are 36 choices for each of 6 positions, repetitions being allowed.

    Of these, there are 26^6 that will contain no digits, and 10^6 that will contain no letters.

    There are therefore 36^6-(26^6+10^6) that each contain at least one letter and one digit.
    Similarly for the 7- and 8- character passwords.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    5
    Thank you very much! I've handed in my answers and now only time will tell
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem involving combinations and permutations
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: June 1st 2011, 11:36 PM
  2. Simple problem combinations permutations...
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: February 19th 2011, 01:28 PM
  3. combinations and permutations problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 29th 2009, 09:13 AM
  4. [SOLVED] Permutations and Combinations problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 13th 2009, 04:13 AM
  5. Permutations and Combinations Problem!! Help!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 24th 2008, 04:35 AM

Search Tags


/mathhelpforum @mathhelpforum