Results 1 to 6 of 6

Math Help - Probability combination!

  1. #1
    Junior Member
    Joined
    Jan 2014
    Posts
    27

    Probability combination!

    Q In how many ways can n things be shared between 2 people.

    Answer is 2^n -2
    And it used
    (1+1)^n
    But i dont get why they use (1+1)^n and im confused with the idea of 'sharing'.

    P.s: how do i solve if it's between 3 people?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,418
    Thanks
    1854

    Re: Probability combination!

    Quote Originally Posted by gahyunkk View Post
    Q In how many ways can n things be shared between 2 people.

    Answer is 2^n -2
    This is incorrect! Call the two people "A" and "B". Suppose n= 1. The one thing can be given to either A or B. There are 2= 2^1, not 2^1- 2= -1, ways to "share". Suppose n= 2. We can give both things to A or give both things to B or give the first to A and the second to B or give the first to B and the second to A. There are 4= 2^2, not 2^2= 2, different ways. In general, there are 2^n, not 2^n- 2, ways to distribute n things among 2 people.

    And it used
    (1+1)^n
    But i dont get why they use (1+1)^n and im confused with the idea of 'sharing'.
    I don't know why they wrote "1+ 1" but that is simply 2^n because there are 2 people.

    P.s: how do i solve if it's between 3 people?
    Pretty much the same way. If there are 3 people, each thing can be given to any one of the 3: there are 3^n ways to do that.
    Last edited by HallsofIvy; August 15th 2014 at 05:26 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2014
    Posts
    27

    Re: Probability combination!

    What if we suppose sharing has to be like two people both must have at least one(=both can't have zero)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Aug 2014
    From
    Poland
    Posts
    40
    Thanks
    7

    Re: Probability combination!

    Then it's like you say, but you didn't assume that.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Feb 2014
    From
    United States
    Posts
    819
    Thanks
    411

    Re: Probability combination!

    Quote Originally Posted by gahyunkk View Post
    Q In how many ways can n things be shared between 2 people.

    Answer is 2^n -2
    And it used
    (1+1)^n
    But i dont get why they use (1+1)^n and im confused with the idea of 'sharing'.

    P.s: how do i solve if it's between 3 people?
    I do not like this problem because the English word "share" is ambiguous. It is debatable whether n to person A and 0 to person B is sharing. In fact it could be construed that if n is even then there is only one way to share, in that A and B each get half, and if n is odd then there are only two ways to share, A gets (n - 1)/2 or (n + 1)/2. Moreover, it makes a difference whether the n objects are distinguishable. What seems to be meant by this problem is how many ways can n distinguishable objects be allocated between 2 people so that each gets something, given n is greater than 0.

    The answer to that question is

    $\displaystyle \sum_{i=1}^{n-1}\dbinom{n}{i} = \left(\sum_{i=0}^n\dbinom{n}{i}\right) - 1 - 1 = (1 + 1)^n - 2 = 2^n - 2.$

    The expansion of (1 + 1)^n gives the binomial coefficients.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2014
    Posts
    27

    Re: Probability combination!

    Ohh thanks !
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability in combination
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 2nd 2012, 10:34 AM
  2. probability with combination
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 16th 2011, 07:31 AM
  3. Probability/ Combination Question | Help!
    Posted in the Statistics Forum
    Replies: 6
    Last Post: April 7th 2010, 12:27 AM
  4. Replies: 2
    Last Post: November 14th 2009, 05:48 AM
  5. Combination Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 25th 2007, 08:13 PM

Search Tags


/mathhelpforum @mathhelpforum