Combination Problem Part 1 about Catalan Number











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Refer to an election in which two candidates Wright and Upshaw ran for dogcatcher. After each vote was tabulated, Wright was never behind Upshaw. This problem is known as the ballot problem.



Suppose that each candidate received exactly $r$ votes. Show that the number of ways the votes could be counted is $C_r$, the $r-$th Catalan number.



My issue with this is, what's the relation between Combinations and the Catalan number? I do have the answer, but I don't understand the logic behind the counting argument.






discrete-mathematics combinations catalan-numbers







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    Refer to an election in which two candidates Wright and Upshaw ran for dogcatcher. After each vote was tabulated, Wright was never behind Upshaw. This problem is known as the ballot problem.



    Suppose that each candidate received exactly $r$ votes. Show that the number of ways the votes could be counted is $C_r$, the $r-$th Catalan number.



    My issue with this is, what's the relation between Combinations and the Catalan number? I do have the answer, but I don't understand the logic behind the counting argument.






    discrete-mathematics combinations catalan-numbers







    share|cite|improve this question









    New contributor




    Aly J is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      up vote
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      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Refer to an election in which two candidates Wright and Upshaw ran for dogcatcher. After each vote was tabulated, Wright was never behind Upshaw. This problem is known as the ballot problem.



      Suppose that each candidate received exactly $r$ votes. Show that the number of ways the votes could be counted is $C_r$, the $r-$th Catalan number.



      My issue with this is, what's the relation between Combinations and the Catalan number? I do have the answer, but I don't understand the logic behind the counting argument.






      discrete-mathematics combinations catalan-numbers







      share|cite|improve this question









      New contributor




      Aly J is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      Refer to an election in which two candidates Wright and Upshaw ran for dogcatcher. After each vote was tabulated, Wright was never behind Upshaw. This problem is known as the ballot problem.



      Suppose that each candidate received exactly $r$ votes. Show that the number of ways the votes could be counted is $C_r$, the $r-$th Catalan number.



      My issue with this is, what's the relation between Combinations and the Catalan number? I do have the answer, but I don't understand the logic behind the counting argument.






      discrete-mathematics combinations catalan-numbers




      discrete-mathematics combinations catalan-numbers






      share|cite|improve this question









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      Aly J is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      share|cite|improve this question









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      edited 23 hours ago









      AspiringMat

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