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In the Pascal family, each child has at least 2 brothers and at least 1 sister. What is the smallest possible number of children in this family?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $7$

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