There are 16 people, they divide into four groups, now from those four groups select a team of three members,such that no two members in the team should belong to same group.
We can select any three of the 4 groups in $^4C_{3}$ ways. Now from each of these groups we can select 1 person in 4 ways.
So total ways = 4 x 4 x 4 x 4 = 256
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