Results 1 to 12 of 12
Like Tree6Thanks
  • 1 Post By Plato
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL

Math Help - Combination Lock Problem

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Combination Lock Problem

    Hey Guys, been a while since I have done a problem as such.

    I have a lock with three selections of numbers, each selection goes 1-30 (giving 30 possible numbers). How many different combinations are possible?

    I used the general An where n is the selections (3) and A is the possible numbers (30) giving me
    An = 303=27,000.

    The next part was tricky, I need to find how many possible numbers when no two numbers can be repeated by any combination.
    I think this is where I use
    P(n,r) = n!/(n-r)!
    which gave me
    30!/(30-3)! = 24360.

    Does this look right to you guys?

    Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1

    Re: Combination Lock Problem

    Both parts are correct.
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Re: Combination Lock Problem

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Combination Lock Problem

    You could use the fundamental counting rule:

    a) 303030 = 27000

    b) 302928 = 24360
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Re: Combination Lock Problem

    Ah yea I saw that.

    Had another question, similar to the one above.
    I have 6 people, how many different ways can I seat the 6 people in six seats?

    Would that just be a 26​=32?

    Or is this a 6! = 720?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Combination Lock Problem

    Using the fundamental counting rule, how many choices do you have for the first seat, second seat, and so on?
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Re: Combination Lock Problem

    ah ok got it. I thought it would be 6!, but it just seemed too big for six numbers. Never really thought about it I guess!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Combination Lock Problem

    Yes 6! is correct. There are n! ways to order n objects.
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Re: Combination Lock Problem

    I can use this same principle with say letters too, e.g. THEORY arranged in any order would be
    6! = 720.

    Then how about it I needed T and H to stay together, but could switch order, e.g. TH and HT are ok. Could I just say...
    1.TH or HT
    2.E
    3.O
    4.R
    5.Y

    Then say 5! = 120, but as TH can also be HT, double the result to give me the answer? so 240 possible orders.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Combination Lock Problem

    Yes, that's correct.
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Oct 2012
    From
    South Dakota
    Posts
    15

    Re: Combination Lock Problem

    Man, you have received a lot of thanks from me today!
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Combination Lock Problem

    Hey, I do appreciate those who click that thanks button, not just for my posts, but for anyone who gives a helpful reply!
    Thanks from RadMabbit
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. combination lock
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: August 28th 2014, 07:24 AM
  2. probality of combination lock HELP!!
    Posted in the New Users Forum
    Replies: 3
    Last Post: November 13th 2012, 07:54 PM
  3. combination lock (question)
    Posted in the Statistics Forum
    Replies: 7
    Last Post: May 18th 2009, 05:08 PM
  4. Master Lock Combination
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 7th 2008, 07:22 PM
  5. Combination Lock
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 1st 2007, 04:11 PM

Search Tags


/mathhelpforum @mathhelpforum