Results 1 to 6 of 6
Like Tree2Thanks
  • 1 Post By Plato
  • 1 Post By Soroban

Math Help - Simple Permutations and Combinations Problem

  1. #1
    Junior Member
    Joined
    Apr 2012
    From
    Mauritius
    Posts
    45
    Thanks
    2

    Angry Simple Permutations and Combinations Problem

    I quote a simple question as follows but having trouble getting to the suggested answer, kinda boring:


    (i) Find the number of ways that a set of 10 different CDs can be shared between Dai and Evan if each receives an odd number of CDs.

    ANS: 512

    Need help on that, Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Simple Permutations and Combinations Problem

    Quote Originally Posted by zikcau25 View Post
    I quote a simple question as follows but having trouble getting to the suggested answer,
    Have a look at this.

    You tell us why that works.
    Thanks from zikcau25
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2012
    From
    Mauritius
    Posts
    45
    Thanks
    2

    Lightbulb Re: Simple Permutations and Combinations Problem

    That what I would understand by " the 10 CDs Shared between Dai and Evan in odd number of CDs" as two separate and odd selections of CDs that always add up to 10 CDs (complementary), each for Dai and Evan.

    I found out these possible5 ways of combining the two selections as follows:

    1. (1_{Dai}, 9_{Evan})

    \binom{10}{1}\times \binom{9}{9}=10

    2. (3_{Dai}, 7_{Evan})

    \binom{10}{3}\times \binom{7}{7}=120

    3. (5_{Dai}, 5_{Evan}) = (5_{Evan}, 5_{Dai})

    \binom{10}{5}\times \binom{5}{5}=252

    4. (7_{Evan}, 3_{Dai})

    \binom{10}{7}\times \binom{3}{3}=120

    5. (9_{Evan}, 1_{Dai})

    \binom{10}{9}\times \binom{1}{1}=10

    Therefore, Sum of all Outcomes = 10+120+252+120+10 = 512
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Simple Permutations and Combinations Problem

    Quote Originally Posted by zikcau25 View Post
    That what I would understand by " the 10 CDs Shared between Dai and Evan in odd number of CDs" as two separate and odd selections of CDs that always add up to 10 CDs (complementary), each for Dai and Evan.
    There is a more systematic way to do this.
    If you have a set of ten there are $2^{10}$ subsets of the set. Half have an even number of elements the other have odd number.
    If Dai gets an odd number of elements then there are an odd number of elements are left for Evan.

    $\dfrac{2^{10}}{2}=2^9=512$
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615

    Re: Simple Permutations and Combinations Problem

    Hello, zikcau25!

    Find the number of ways that a set of 10 different CDs
    can be shared by Dai and Evan if each receives an odd number of CDs.

    . . \begin{array}{ccccc} \text{Dai} & \text{Evan} \\ \hline 1 & 9 & {10\choose1,9} &=& \;10 \\ 3&7 & {10\choose3,7} &=& 120 \\ 5&5 & {10\choose5,5} &=& 252 \\ 7&3 & {10\choose7,3} &=& 120 \\ 9&1 & {10\choose9,1} &=& \;10 \\ \hline &&&& 512\end{array}
    Thanks from zikcau25
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2012
    From
    Mauritius
    Posts
    45
    Thanks
    2

    Re: Simple Permutations and Combinations Problem

    Thanks for the correction.
    I think I was wrong in swapping the names in the other half, because the list is naturally symmetrical.
    Now it looks clearer and direct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem involving combinations and permutations
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: June 1st 2011, 11:36 PM
  2. Simple problem combinations permutations...
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: February 19th 2011, 01:28 PM
  3. Permutations and Combinations problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 3rd 2009, 08:17 PM
  4. combinations and permutations problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 29th 2009, 09:13 AM
  5. Permutations and Combinations Problem!! Help!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 24th 2008, 04:35 AM

Search Tags


/mathhelpforum @mathhelpforum