Results 1 to 3 of 3

Math Help - [SOLVED] Help with some bit string counting questions

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    232

    [SOLVED] Help with some bit string counting questions

    I don't have any issues with calculation on these problems, but I worry that the semantics of these problems may change how they are meant to be calculated. I've provided the questions and my current answers.

    How many bit strings of length 16 contain

    a) Exactly 4 more ones than zeros?
    Current answer: \frac{16!}{10!6!}=8008

    b) Exactly 2 ones and 14 zeros?
    Current answer: \frac{16!}{14!2!}=120

    c) Three times as many ones as zeros?
    Current answer: \frac{16!}{4!12!}=1820

    I can't shake the feeling that the way these questions are worded changes their meaning. Can someone confirm my answers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Quote Originally Posted by Runty View Post
    How many bit strings of length 16 contain
    a) Exactly 4 more ones than zeros?
    Current answer: \frac{16!}{10!6!}=8008

    b) Exactly 2 ones and 14 zeros?
    Current answer: \frac{16!}{14!2!}=120

    c) Three times as many ones as zeros?
    Current answer: \frac{16!}{4!12!}=1820
    They are correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    232
    Quote Originally Posted by Plato View Post
    They are correct.
    Thanks for helping me make sure of that. I wasn't entirely sure of the semantics, so I needed to confirm it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. how many committees? (counting questions...)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 29th 2011, 06:08 AM
  2. String counting questions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 26th 2010, 06:06 AM
  3. String of questions.. confused...
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 3rd 2008, 08:28 AM
  4. Replies: 4
    Last Post: October 21st 2008, 11:17 AM
  5. Averages, Counting, and other questions (help?)
    Posted in the Math Topics Forum
    Replies: 9
    Last Post: February 25th 2008, 11:26 AM

Search Tags


/mathhelpforum @mathhelpforum