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Problem 87

Combinatorics Difficulty 1.2 Multiple choice CEMC Pascal · Canada · 2024

There are $20$ students in a
class. In total, $10$ of them have
black hair, $5$ of them wear glasses,
and $3$ of them both have black hair
and wear glasses. How many of the students have black hair but do not
wear glasses?

Pick one

Official solution

Katie’s total time is equal to the sum of $3$ minutes and $45$ seconds and $4$ minutes and $35$ seconds. Adding $45$ seconds and $35$ seconds, we get $45+35=80$ seconds. Since there are $60$ seconds in $1$ minute, then $80$ seconds is equal to $1$ minute and $20$ seconds. Thus, Katie’s total time was
$3+4+1=8$ complete minutes plus $20$ seconds, for a total of $8$ minutes and $20$ seconds.

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