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, 2011

Combinatorics Difficulty 2.0 Junior Find the answer Canada

A $51$ cm rod is built from $5$ cm rods and $2$ cm rods. All of the $5$ cm rods must come first, and are followed by the $2$ cm rods. For example, the rod could be made from seven $5$ cm rods followed by eight $2$ cm rods. How many ways are there to build the $51$ cm rod?

(A) $5$ (B) $6$ (C) $7$ (D) $8$ (E) $9$

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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.