2021 AMC 12B Problem 2
Problem 2 of 25EasierNumber TheoryCombinatorics
At a math contest, students are wearing blue shirts, and another students are wearing yellow shirts. The students are assigned into pairs. In exactly of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
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Solution
The all-blue pairs account for blue students, leaving blue students.
Each of those blue students must be paired with a yellow student, so there are mixed pairs, using yellow students.
The remaining yellow students form all-yellow pairs.
Thus, the correct answer is B.
Tagged: basic counting · parity