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Senior 3-ways

On March 16, the College Board's online question of the day read as follows:  "In a class of 80 seniors, there are 3 boys for every 5 girls. In the junior class, there are..." blah, blah, blah...BORING. Today, the BSAT "re-purposes" this promising setup...

In a class of 80 seniors, there are 3 boys for every 5 girls. What is the greatest number of 3-ways involving at least 1 member of each sex that can be assembled from this class?

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Thank you, Calvin Klein, for an ad campaign as offensive as the College Board's question of the day is boring.

LOVE AND SEX

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