2024 AMC 8 Problems/Problem 7

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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?

$\textbf{(A) } 21 \qquad \textbf{(B) } 37 \qquad \textbf{(C) } 42 \qquad \textbf{(D) } 44 \qquad \textbf{(E) } 259$

Solution 1