Results 1 to 3 of 3

Thread: Arrangements of SUCCESS

  1. #1
    Newbie
    Joined
    Nov 2017
    From
    Manchester NH
    Posts
    1

    Arrangements of SUCCESS

    To find how many arrangements contain the two C's next to each other, I considered them as a unit and got 6!/3!=720/6=120.
    I actually wrote them out and counted them to verify.
    To find out how many arrangements containing the two C's also contain two or more S's next to each other, I considered each pair as a unit and got 5!=120.

    Obviously, this isn't correct. in my actual count I only found 96.

    What is the correct way to find the answer?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,691
    Thanks
    318

    Re: Arrangements of SUCCESS

    SUCCESS = 1233411 ; easier...

    Lowest arrangement: 1112334
    highest: 4332111
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,454
    Thanks
    2728
    Awards
    1

    Re: Arrangements of SUCCESS

    Quote Originally Posted by thayer View Post
    To find out how many arrangements containing the two C's also contain two or more S's next to each other, I considered each pair as a unit and got 5!=120.
    I will assume that all seven letters and the C's need not be together.
    Find the number of arrangements in which none of the S's are together:
    $__U__C__C__E__$ there are four places to place the S's so as to separate them.
    There are $\dbinom {4}{3}=4$ ways, the separators can be arranged in $\dfrac{4!}{2!}$ ways.

    So the answer is $\dfrac{7!}{2!\cdot3!}-4\cdot\dfrac{4!}{2!}$ YOU MUST EXPLAIN WHY TO US.
    Note: my answer does not assume the C's are together.
    You wrote "containing the two C's also contain two or more S's next to each other,
    Last edited by Plato; Nov 4th 2017 at 09:01 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. success arrangement
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Aug 20th 2011, 11:13 AM
  2. Success Probabilty
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Dec 6th 2009, 06:56 PM
  3. probability of success
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Feb 19th 2009, 01:09 AM

/mathhelpforum @mathhelpforum