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
edited 23 hours ago
AspiringMat
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Aly J
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up vote
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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
edited 23 hours ago
AspiringMat
478518
asked yesterday
Aly J
61
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.
add a comment |
up vote
1
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
edited 23 hours ago
AspiringMat
478518
asked yesterday
Aly J
61
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
edited 23 hours ago
AspiringMat
478518
asked yesterday
Aly J
61
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.
edited 23 hours ago
AspiringMat
478518
asked yesterday
Aly J
61
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.
edited 23 hours ago
AspiringMat
478518
edited 23 hours ago
AspiringMat
478518
edited 23 hours ago
AspiringMat
478518
478518
asked yesterday
Aly J
61
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.
asked yesterday
Aly J
61
asked yesterday
Aly J
61
61
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.
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.
Aly J is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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Aly J is a new contributor. Be nice, and check out our Code of Conduct.
Aly J is a new contributor. Be nice, and check out our Code of Conduct.
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