Results 1 to 2 of 2

Thread: Counting - Discrete math

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    26

    Counting - Discrete math

    7 woman and 9 man are on the faculty in the math department in the school.

    (1) How many ways are there to select a committee of five members of the department if at least one woman must be on the same committee ?

    (2) how many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee .

    Can some one please help me with this ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    You are considering a set which has $\displaystyle 16$ elements, and has a partition in two subsets $\displaystyle A$ and $\displaystyle B$ which have $\displaystyle 7$ and $\displaystyle 9$ elements.

    For 1), what you want to know is the number of 5-element subsets of $\displaystyle E$ that have at least one element in $\displaystyle A$. That means the "first" element $\displaystyle x$ must be in $\displaystyle A$, you have $\displaystyle 7$ choices, then every subset with $\displaystyle 4$ elements in $\displaystyle A-\{x\}$ union $\displaystyle \{x\}$ is a solution.
    So there are $\displaystyle 7\times C^{4}_{15}$ possible committees.

    2) can be done is a similar way.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The Math Behind Card Counting
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 8th 2011, 07:48 PM
  2. Counting, Probability, Trees, etc in Discrete Math
    Posted in the Discrete Math Forum
    Replies: 16
    Last Post: Dec 1st 2010, 12:58 PM
  3. SAT Math Counting Problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Sep 5th 2010, 11:11 AM
  4. Discrete Math Help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 12th 2009, 04:15 PM
  5. Discrete Math
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Apr 26th 2007, 08:49 AM

Search Tags


/mathhelpforum @mathhelpforum