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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

How many different combinations of pennies, nickels, dimes and quarters use $48$ coins to total $\$1.00$ ?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $8$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.