Difference between revisions of "2024 AMC 8 Problems/Problem 7"

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==Problem==
 
==Problem==
  
A person is playing one turn in a card-based game. They can play Card A for 1 point, Card B for 2 points, and Card C for 3 points. If order of the cards doesn't matter, how many possible ways are there to play one turn with 20 points considering that that there is an unlimited amount of each card?
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A person is playing one turn in a card-based game. They can play Card A for 1 point, Card B for 2 points, and Card C for 3 points. If order of the cards doesn't matter, how many possible ways are there to play one turn using up a total of 20 points considering that that there is an unlimited amount of each card?
  
 
<math>\textbf{(A) } 21 \qquad \textbf{(B) } 37 \qquad \textbf{(C) } 43 \qquad \textbf{(D) } 44 \qquad \textbf{(E) } 259</math>
 
<math>\textbf{(A) } 21 \qquad \textbf{(B) } 37 \qquad \textbf{(C) } 43 \qquad \textbf{(D) } 44 \qquad \textbf{(E) } 259</math>

Revision as of 19:28, 22 January 2024

Problem

A person is playing one turn in a card-based game. They can play Card A for 1 point, Card B for 2 points, and Card C for 3 points. If order of the cards doesn't matter, how many possible ways are there to play one turn using up a total of 20 points considering that that there is an unlimited amount of each card?

$\textbf{(A) } 21 \qquad \textbf{(B) } 37 \qquad \textbf{(C) } 43 \qquad \textbf{(D) } 44 \qquad \textbf{(E) } 259$


Note: This is not one of the AMC 8 2024 questions.

Solution 1