Difference between revisions of "2020 AMC 12B Problems/Problem 15"

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15. There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him,as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other?
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==Problem==
  
<math>(A) 11 (B) 12 (C) 13 (D) 14 (E)  15</math>
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There are <math>10</math> people standing equally spaced around a circle. Each person knows exactly <math>3</math> of the other <math>9</math> people: the <math>2</math> people standing next to her or him,as well as the person directly across the circle. How many ways are there for the <math>10</math> people to split up into 5<math> pairs so that the members of each pair know each other?
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</math>(A) 11<math> </math>(B) 12<math> </math>(C) 13<math> </math>(D) 14<math> </math>(E)  15$

Revision as of 21:18, 7 February 2020

Problem

There are $10$ people standing equally spaced around a circle. Each person knows exactly $3$ of the other $9$ people: the $2$ people standing next to her or him,as well as the person directly across the circle. How many ways are there for the $10$ people to split up into 5$pairs so that the members of each pair know each other?$(A) 11$$ (Error compiling LaTeX. Unknown error_msg)(B) 12$$ (Error compiling LaTeX. Unknown error_msg)(C) 13$$ (Error compiling LaTeX. Unknown error_msg)(D) 14$$ (Error compiling LaTeX. Unknown error_msg)(E) 15$