Select $n$ items out of $N$ with replacement

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite
1












Select a subset of $n$ items out of $N$ with replacement and repeat $r$ times.
(This can be done in $N choose n^r$ ways, right?)



What is the probability that $k$ elements are contained in each subset selected?
So we have chosen $r$ subsets of $n$ elements. If we want $k$ fixed then we get $$fracN-k choose n-k^rN choose n^r$$



Is this correct?







share|cite|improve this question


























    up vote
    2
    down vote

    favorite
    1












    Select a subset of $n$ items out of $N$ with replacement and repeat $r$ times.
    (This can be done in $N choose n^r$ ways, right?)



    What is the probability that $k$ elements are contained in each subset selected?
    So we have chosen $r$ subsets of $n$ elements. If we want $k$ fixed then we get $$fracN-k choose n-k^rN choose n^r$$



    Is this correct?







    share|cite|improve this question
























      up vote
      2
      down vote

      favorite
      1









      up vote
      2
      down vote

      favorite
      1






      1





      Select a subset of $n$ items out of $N$ with replacement and repeat $r$ times.
      (This can be done in $N choose n^r$ ways, right?)



      What is the probability that $k$ elements are contained in each subset selected?
      So we have chosen $r$ subsets of $n$ elements. If we want $k$ fixed then we get $$fracN-k choose n-k^rN choose n^r$$



      Is this correct?







      share|cite|improve this question














      Select a subset of $n$ items out of $N$ with replacement and repeat $r$ times.
      (This can be done in $N choose n^r$ ways, right?)



      What is the probability that $k$ elements are contained in each subset selected?
      So we have chosen $r$ subsets of $n$ elements. If we want $k$ fixed then we get $$fracN-k choose n-k^rN choose n^r$$



      Is this correct?









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 20 at 13:03

























      asked Aug 20 at 8:02









      mandella

      713420




      713420




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          1
          down vote













          1. Yes.

          2. No, it should also be multiplied by $k!$, since you can have a permutation of this subset.





          share|cite|improve this answer






















          • Oh that is true. Thank you very much!
            – mandella
            Aug 20 at 8:29










          • do you have time to chat because I have another question for this one
            – mandella
            Aug 20 at 8:31










          • in a few hours maybe
            – pointguard0
            Aug 20 at 8:36










          • until then could you help me more with the other question please
            – mandella
            Aug 20 at 8:36










          • chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
            – pointguard0
            Aug 20 at 14:13










          Your Answer




          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );








           

          draft saved


          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888519%2fselect-n-items-out-of-n-with-replacement%23new-answer', 'question_page');

          );

          Post as a guest






























          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          1
          down vote













          1. Yes.

          2. No, it should also be multiplied by $k!$, since you can have a permutation of this subset.





          share|cite|improve this answer






















          • Oh that is true. Thank you very much!
            – mandella
            Aug 20 at 8:29










          • do you have time to chat because I have another question for this one
            – mandella
            Aug 20 at 8:31










          • in a few hours maybe
            – pointguard0
            Aug 20 at 8:36










          • until then could you help me more with the other question please
            – mandella
            Aug 20 at 8:36










          • chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
            – pointguard0
            Aug 20 at 14:13














          up vote
          1
          down vote













          1. Yes.

          2. No, it should also be multiplied by $k!$, since you can have a permutation of this subset.





          share|cite|improve this answer






















          • Oh that is true. Thank you very much!
            – mandella
            Aug 20 at 8:29










          • do you have time to chat because I have another question for this one
            – mandella
            Aug 20 at 8:31










          • in a few hours maybe
            – pointguard0
            Aug 20 at 8:36










          • until then could you help me more with the other question please
            – mandella
            Aug 20 at 8:36










          • chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
            – pointguard0
            Aug 20 at 14:13












          up vote
          1
          down vote










          up vote
          1
          down vote









          1. Yes.

          2. No, it should also be multiplied by $k!$, since you can have a permutation of this subset.





          share|cite|improve this answer














          1. Yes.

          2. No, it should also be multiplied by $k!$, since you can have a permutation of this subset.






          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Aug 20 at 13:55

























          answered Aug 20 at 8:29









          pointguard0

          1,236821




          1,236821











          • Oh that is true. Thank you very much!
            – mandella
            Aug 20 at 8:29










          • do you have time to chat because I have another question for this one
            – mandella
            Aug 20 at 8:31










          • in a few hours maybe
            – pointguard0
            Aug 20 at 8:36










          • until then could you help me more with the other question please
            – mandella
            Aug 20 at 8:36










          • chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
            – pointguard0
            Aug 20 at 14:13
















          • Oh that is true. Thank you very much!
            – mandella
            Aug 20 at 8:29










          • do you have time to chat because I have another question for this one
            – mandella
            Aug 20 at 8:31










          • in a few hours maybe
            – pointguard0
            Aug 20 at 8:36










          • until then could you help me more with the other question please
            – mandella
            Aug 20 at 8:36










          • chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
            – pointguard0
            Aug 20 at 14:13















          Oh that is true. Thank you very much!
          – mandella
          Aug 20 at 8:29




          Oh that is true. Thank you very much!
          – mandella
          Aug 20 at 8:29












          do you have time to chat because I have another question for this one
          – mandella
          Aug 20 at 8:31




          do you have time to chat because I have another question for this one
          – mandella
          Aug 20 at 8:31












          in a few hours maybe
          – pointguard0
          Aug 20 at 8:36




          in a few hours maybe
          – pointguard0
          Aug 20 at 8:36












          until then could you help me more with the other question please
          – mandella
          Aug 20 at 8:36




          until then could you help me more with the other question please
          – mandella
          Aug 20 at 8:36












          chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
          – pointguard0
          Aug 20 at 14:13




          chat.stackexchange.com/rooms/info/81944/probability?tab=general please enter here if you want to ask more questions.
          – pointguard0
          Aug 20 at 14:13












           

          draft saved


          draft discarded


























           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888519%2fselect-n-items-out-of-n-with-replacement%23new-answer', 'question_page');

          );

          Post as a guest













































































          這個網誌中的熱門文章

          How to combine Bézier curves to a surface?

          Why am i infinitely getting the same tweet with the Twitter Search API?

          Is there any way to eliminate the singular point to solve this integral by hand or by approximations?