Difference between revisions of "2021 AMC 10B Problems/Problem 22"
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| − | + | ==Problem== | |
| + | Ang, Ben, and Jasmin each have <math>5</math> blocks, colored red, blue, yellow, white, and green; and there are <math>5</math> empty boxes. Each of the people randomly and independently of the other two people places one of their blocks into each box. The probability that at least one box receives <math>3</math> blocks all of the same color is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m + n ?</math> | ||
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| + | <math>\textbf{(A)} ~47 \qquad\textbf{(B)} ~94 \qquad\textbf{(C)} ~227 \qquad\textbf{(D)} ~471 \qquad\textbf{(E)} ~542</math> | ||
| + | ==Solution== | ||
Revision as of 19:43, 11 February 2021
Problem
Ang, Ben, and Jasmin each have 
blocks, colored red, blue, yellow, white, and green; and there are empty boxes. Each of the people randomly and independently of the other two people places one of their blocks into each box. The probability that at least one box receives 
blocks all of the same color is 
, where 
and 
are relatively prime positive integers. What is 
