CIMC 2022 Part A - Question 6, CEMC UWaterloo

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Difficulty: 6

This problem is tagged with cimc, cimc22, highschool.

(Canadian Intermediate Mathematics Contest 2022, Part A, Question 6, CEMC - UWaterloo)

How many ways are there to choose integers $a$, $b$ and $c$ with $a \lt b \lt c$ from the list $1, 5, 8, 21, 22, 27, 30, 33, 37, 39, 46, 50$ so that the product $abc$ is a multiple of $12$?

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