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Twins triplets handshake counting

1425ApprenticeCombinatoricsCounting Principles

AMC 12A · 2011 · Problem 9

At a twins and triplets convention, there were $9$ sets of twins and $6$ sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

Answer choices

A
324
B
441
C
630
D
648
E
882
0 students attempted0% solvedRating 1425

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