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Problem 745

AMC 12 late, AIME early

Combinatorics Difficulty 4.0 Find the answer BMO Round 1 · United Kingdom · 2006

Adrian teaches a class of six pairs of twins. He wishes to set up teams for a quiz, but wants to avoid putting any pair of twins into the same team. Subject to this condition:

i) In how many ways can he split them into two teams of six?

ii) In how many ways can he split them into three teams of four?

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