2021 Fall AMC 10B Problems

  • 1 Problem 1
  • 2 Problem 2
  • 3 Problem 3
  • 4 Problem 4
  • 5 Problem 5
  • 6 Problem 6
  • 7 Problem 7
  • 8 Problem 8
  • 9 Problem 9
  • 10 Problem 10
  • 11 Problem 11
  • 12 Problem 12
  • 13 Problem 13
  • 14 Problem 14
  • 15 Problem 15
  • 16 Problem 16
  • 17 Problem 17
  • 18 Problem 18
  • 19 Problem 19
  • 20 Problem 20
  • 21 Problem 21
  • 22 Problem 22
  • 23 Problem 23
  • 24 Problem 24
  • 25 Problem 25
  • 26 See also

$1234+2341+3412+4123?$

Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris's. What is the expected number of balls that occupy their original positions after these two successive transpositions?

$(\textbf{A})\: 1.6\qquad(\textbf{B}) \: 1.8\qquad(\textbf{C}) \: 2.0\qquad(\textbf{D}) \: 2.2\qquad(\textbf{E}) \: 2.4$

  • AMC 10 Problems and Solutions
  • Mathematics competitions
  • Mathematics competition resources

AMC logo.png

  • AMC 10 Problems

Something appears to not have loaded correctly.

Click to refresh .

art of problem solving amc 10 practice tests

Mathematical Association of America

Sample competition: 2022 amc 10 a.

Test out your creative problem-solving skills! Try your hand at these problems from the 2022 American Mathematics Competition (AMC) 10 A competition. This mathematical competition is for students in grades 10 and below.

Interested in more? You can purchase collections of past competitions from our store or participate in our next MAA AMC competition .

IMAGES

  1. amc 10 problems

    art of problem solving amc 10 practice tests

  2. Art of problem solving amc 10 questions

    art of problem solving amc 10 practice tests

  3. Art of Problem Solving: 2019 AMC 10 A #22

    art of problem solving amc 10 practice tests

  4. Art of Problem Solving

    art of problem solving amc 10 practice tests

  5. Art of Problem Solving

    art of problem solving amc 10 practice tests

  6. Art of Problem Solving

    art of problem solving amc 10 practice tests

VIDEO

  1. Art of Problem Solving: 2019 AMC 10 A #25 / AMC 12 A #24

  2. Art of Problem Solving: 2020 AMC 10 A #21 / AMC 12 A #19

  3. Art of Problem Solving: 2019 AMC 10 A #22

  4. Art of Problem Solving: 2020 AMC 10 A #22

  5. Art of Problem Solving: 2020 AMC 10 A #25 / AMC 12 A #23

  6. Art of Problem Solving: 2018 AMC 10 A #23 / AMC 12 A #17