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counting and probability senior

Problem

At a twins and triplets convention, there were sets of twins and 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?
(A)
(B)
(C)
(D)
Solution
There are total twins and total triplets. Each of the twins shakes hands with the twins not in their family and of the triplets, a total of people. Each of the triplets shakes hands with the triplets not in their family and of the twins, for a total of people. Dividing by two to accommodate the fact that each handshake was counted twice, we get a total of
Final answer
B