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2021 AMC Fall 10A Problem 21

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2021 AMC Fall 10A Problem 21AMC 10 Step by Step

Name: Date: September 13, 2026

Basic Counting · difficulty 3 of 5 · about 5 min · position P21-25

Each of the $20$ balls is tossed independently and at random into one of the $5$ bins. Let $p$ be the probability that some bin ends up with $3$ balls, another with $5$ balls, and the other three with $4$ balls each. Let $q$ be the probability that every bin ends up with $4$ balls. What is $\frac{p}{q}$ ?

A)
$1$
B)
$4$
C)
$8$
D)
$12$
E)
$16$

2021 AMC Fall 10A Problem 21

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