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

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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 <math>5</math> pairs so that the members of each pair know each other?
 
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 <math>5</math> pairs so that the members of each pair know each other?
  
<math>(A)</math>  <math>11</math> <math>(B)</math>  <math>12</math> <math>(C)</math> <math>13</math> <math>(D)</math>  <math>14</math> <math>(E)</math>  <math>15</math>
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<math>\textbf{(A)}\ 11 \qquad\textbf{(B)}\ 12 \qquad\textbf{(C)}\ 13 \qquad\textbf{(D)}\ 14 \qquad\textbf{(E)}\ 15</math>

Revision as of 22:20, 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?

$\textbf{(A)}\ 11 \qquad\textbf{(B)}\ 12 \qquad\textbf{(C)}\  13 \qquad\textbf{(D)}\ 14 \qquad\textbf{(E)}\ 15$