2025 AMC 8 Problems/Problem 9

There are $10$ matchsticks on the table. Percy takes $1$ , $2$ or $3$ matchsticks each time. How many ways are there for him to take all the matchsticks?

$\textbf{(A)}\ 274 \qquad \textbf{(B)}\ 275 \qquad \textbf{(C)}\ 276 \qquad \textbf{(D)}\ 280 \qquad \textbf{(E)}\ 295$

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2025 AMC 8 Problems/Problem 9