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, 2000

Combinatorics Difficulty 2.0 Junior Find the answer Canada

The digits 1, 1, 2, 2, 3, and 3 are arranged to form an odd six digit integer. The 1's are separated by one digit, the 2's by two digits, and the 3's by three digits. What are the last three digits of this integer?

(A) $312$ (B) $123$ (C) $131$ (D) $121$ (E) $213$

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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.