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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Miss Spelling, the English teacher, asked five of her students how many of the five of them had done their homework the day before. Daniel said none, Ellen said only one, Cara said exactly two, Zain said exactly three and Marcus said exactly four. Miss Spelling knew that the students who had not done their homework were not telling the truth but those who had done their homework were telling the truth. How many of these students had done their homework the day before?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $5$

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