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2010 AMC 10B Problem 18

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2010 AMC 10B Problem 18AMC 10 Step by Step

Name: Date: September 13, 2026

Modular Arithmetic · difficulty 3 of 5 · about 5 min · position P16-20

Positive integers $a$ , $b$ , and $c$ are randomly and independently selected with replacement from the set $\{1, 2, 3,\dots, 2010\}$ . What is the probability that $abc + ab + a$ is divisible by $3$ ?

A)
$\dfrac{1}{3}$
B)
$\dfrac{29}{81}$
C)
$\dfrac{31}{81}$
D)
$\dfrac{11}{27}$
E)
$\dfrac{13}{27}$

2010 AMC 10B Problem 18

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