Difference between revisions of "2021 Fall AMC 10A Problems/Problem 21"
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Each of the <math>20</math> balls is tossed independently and at random into one of the <math>5</math> bins. Let <math>p</math> be the probability that some bin ends up with <math>3</math> balls, another with <math>5</math> balls, and the other three with <math>4</math> balls each. Let <math>q</math> be the probability that every bin ends up with <math>4</math> balls. What is <math>\frac{p}{q}</math>? | Each of the <math>20</math> balls is tossed independently and at random into one of the <math>5</math> bins. Let <math>p</math> be the probability that some bin ends up with <math>3</math> balls, another with <math>5</math> balls, and the other three with <math>4</math> balls each. Let <math>q</math> be the probability that every bin ends up with <math>4</math> balls. What is <math>\frac{p}{q}</math>? | ||
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| + | <math>\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ | ||
| + | 12 \qquad\textbf{(E)}\ 16</math> | ||
Revision as of 17:36, 22 November 2021
Each of the 
balls is tossed independently and at random into one of the 
bins. Let 
be the probability that some bin ends up with 
balls, another with balls, and the other three with 
balls each. Let 
be the probability that every bin ends up with balls. What is 
?
