Results 1 to 2 of 2

Thread: Counting using inclusion/exclusion principle.

  1. #1
    Member
    Joined
    Feb 2011
    Posts
    83
    Thanks
    2

    Counting using inclusion/exclusion principle.

    I am interested in arrangements of MATHEMATICS
    with

    both T's before both A's or
    both A's before both M's or
    both M's before the E


    I define the following sets

    $\displaystyle A_1$ = {arrangements with both T's before both A's}

    $\displaystyle A_2$ = {arrangements with both A's before both M's}

    $\displaystyle A_3$ = {arrangements with both M's before E}

    I am able to find the cardinality of everything else but $\displaystyle A_1 \cap A_3$

    i.e. arrangements with both T's before both A's and both M's before E.

    I know I want to pick four of the 11 spots (11 choose 4)

    and arrange H,I,C,S in those spots (4! ways)

    But I dont know whaat to do next, I can't place only the T's in the two left most spots because certainly go T,M,M,E,T.

    Thank you for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,742
    Thanks
    2814
    Awards
    1

    Re: Counting using inclusion/exclusion principle.

    Quote Originally Posted by Jame View Post
    I am interested in arrangements of MATHEMATICS with
    both T's before both A's or
    both A's before both M's or
    both M's before the E
    I define the following sets
    $\displaystyle A_1$ = {arrangements with both T's before both A's}
    $\displaystyle A_2$ = {arrangements with both A's before both M's}
    $\displaystyle A_3$ = {arrangements with both M's before E}
    I am able to find the cardinality of everything else but $\displaystyle A_1 \cap A_3$
    Surely $\displaystyle \|A_1 \cap A_3\|=\binom{11}{4}(4!)\binom{7}{4}$.

    i.e. Place the $\displaystyle \{H,I,C,S\}$ and arrange; select the four places to place $\displaystyle \{T,T,A,A\}$(only one way); finally put the $\displaystyle \{M,M,E\}$ is the remaining three places.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inclusion–exclusion principle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Nov 22nd 2011, 05:45 AM
  2. Counting using inclusion/exclusion principle.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 12th 2011, 09:26 AM
  3. inclusion exclusion principle help!
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Aug 9th 2011, 06:17 AM
  4. Inclusion - Exclusion Principle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Mar 15th 2011, 06:52 AM
  5. Principle of Inclusion of Exclusion
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Dec 10th 2008, 12:15 PM

/mathhelpforum @mathhelpforum