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2021 AMC Fall 10B Problem 16

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2021 AMC Fall 10B Problem 16AMC 10 Step by Step

Name: Date: September 13, 2026

Expected Value · difficulty 3 of 5 · about 5 min · position P16-20

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?

A)
$1.6$
B)
$1.8$
C)
$2.0$
D)
$2.2$
E)
$2.4$

2021 AMC Fall 10B Problem 16

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