Results 1 to 7 of 7

Math Help - sampling problem

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    26

    sampling problem

    hello
    the problem is that suppose i have n distinct balls(or anything) in a box..i have to take r samples ...i.e i have to pick r balls out of those n one by one ...now there are four cases
    1.i take the the mth ball without replacing the previous m-1 balls and the sequence in which i take the balls matters
    2.same as one but here the sequence doesnot matter
    3. i replace the previously taken balls before picking out the next one and the sequence in which they come out matters
    4.same as 3 but the sequence doesnot matter

    problem is that in each case in how many possible ways the balls can be organized ...or we can say that in each case how many elements are there in sample space ....

    now first three cases i have a general solution for them and i understand them ...but in case of 4th i know the answer but dont know how it came up
    ..the ans is
    <br />
\binom{n+r-1}{r}<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1759
    Awards
    1
    \binom{n+r-1}{r} is the number of ways to select r items from a variety of n different kinds (each kind has at least r available items).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    26
    i dont understand wat u r trying to say and how it proves the 4th ;part...
    <br />
\binom{n+r-1}{r}<br />

    this means that we have total of n+r-1 objects and we have to choose r out of them and the sequence doesnot matter to us ...

    waiting for a clarification
    thanx
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1759
    Awards
    1
    Quote Originally Posted by corleone2463 View Post
    i dont understand wat u r trying to say and how it proves the 4th ;part...
    <br />
\binom{n+r-1}{r}<br />
    Suppose that you go into an ice cream shop which offers twenty-one flavors of ice cream.
    They have a special on, a plate of five scoops of any and all flavors.
    For example: I would order two scoops of chocolate, two scoops of vanilla and one of strawberry.
    How many different selections are possible?
    Answer: \binom{5+21-1}{5}
    This is known as multi-selections \binom{K+N-1}{K} select K items from N difference possibilities.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2009
    Posts
    26
    yeah i know that but im asking a proof of that the no of possibilities actualy equals to that factorial
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1759
    Awards
    1
    Quote Originally Posted by corleone2463 View Post
    but im asking a proof of that the no of possibilities actualy equals to that factorial
    Ok, here is the proof.
    If we want to know the number of way to put K identical objects into N different cells that can be modeled using K o’s and N-1 ‘|’.
    For example: put five identical balls into three named cells.
    This model o|ooo|o says put one ball in the A cell, three in the B cell and one in the C cell.

    This model oooo||o says put four balls in the A cell, none in the B cell and one in the C cell.

    So any rearrangement of the string ooooo|| represents one way to put those five identical balls into three different cells.
    The number of ways to rearrange that string is \frac{7!}{(5!)(2!)}=\binom{5+3-1}{5}.

    To generalize, the number of ways to put K identical objects into N different cells is
    \binom{K+N-1}{K}.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Feb 2009
    Posts
    26
    thankyou very much ...this is a good and simple proof
    can you suggest some such interesting problems like this one to solve in probability
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability Sampling and Sampling Methods
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: March 16th 2011, 05:41 AM
  2. Sampling Distribution Problem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 2nd 2010, 05:20 PM
  3. help with a sampling variance problem
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 3rd 2009, 07:54 PM
  4. Random Sample of Movies (Sampling Problem)
    Posted in the Statistics Forum
    Replies: 0
    Last Post: October 13th 2009, 06:05 PM
  5. sampling problem for scale free networks
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: July 14th 2009, 01:07 AM

Search Tags


/mathhelpforum @mathhelpforum