Results 1 to 10 of 10

Math Help - More Fundamental Counting

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    23

    More Fundamental Counting

    How many seven-letter words contain at least one X?

    How many seven-letter words contain at least two X's?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by kturf View Post
    How many seven-letter words contain at least one X?

    How many seven-letter words contain at least two X's?
    Once again, what. do. you. think?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    23

    Here's what I think...

    At least one X:
    26!/6!(26-6)! + 25!/(25-5)! + .... 22!/(22-2)! + 1

    At least 2 X's would begin at 25...

    Is that right? Or is it something to do with 26^7 minus something?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by kturf View Post
    At least one X:
    is it something to do with 26^7 minus something?
    Hint: There are 25^7 that contain no X.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    23
    So would it be 25^6 that contain 1 X and 25^5 that contain 2 X's?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by kturf View Post
    So would it be 25^6 that contain 1 X and 25^5 that contain 2 X's?
    Absolutely not.
    Contains exactly one X: 7\cdot 25^6.

    In order to receive further help, you must reply with an explanation of why that is the correct answer.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    23
    For a word with 7 letters and exactly one X, the answer is 7 times 25^6 because you have seven spots available and 25 other possible letters for the 6 spots that are not the X.

    So, for one or more X's, the answer would be

    7 times 25^6 + 7 times 25^5 + 7 times 25^4 + 7 times 25^3 + 7 times 25^2 + 7 times 25 + 1?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by kturf View Post
    How many seven-letter words contain at least two X's?
    26^7-25^7-7\cdot 25^6 WHY?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2009
    Posts
    23
    If you could explain why, that would be very helpful.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by kturf View Post
    If you could explain why, that would be very helpful.
    26^7 the total.
    25^7 contains no X.
    7\cdot 25^6 contains exactly one X.
    26^7-25^7-7\cdot 25^6 remove those two from the total.
    What do you have left?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fundamental Counting principle problem
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 4th 2011, 01:20 PM
  2. Fundamental Counting Principles
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: January 12th 2010, 07:26 AM
  3. probability and fundamental counting principle?
    Posted in the Statistics Forum
    Replies: 3
    Last Post: March 24th 2008, 05:48 PM
  4. fundamental counting principal
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 9th 2007, 02:56 PM
  5. re:premutations and fundamental counting principals
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: December 13th 2005, 12:14 PM

Search Tags


/mathhelpforum @mathhelpforum