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Problem 141

Combinatorics Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2012

At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are $d$ doctors and $n$ nurses at the hospital. The product of $d$ and $n$ is

Pick one

Official solution

Since Emily is a doctor and there are 5 doctors and 3 nurses aside from Emily at the hospital, then there are 6 doctors and 3 nurses in total.

Since Robert is a nurse, then aside from Robert, there are 6 doctors and 2 nurses.

Therefore, $d=6$ and $n=2$ , so $dn=12$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.