Engineering Board Exam Reviewer · Circular and Cyclic Permutations · medium

In how many ways can 4 Americans and 3 Filipinos be seated around a circular table if all the Filipinos must sit together?

  1. 720
  2. 5,040
  3. 288
  4. 144

Answer

D. 144

Solution

Treat the 3 Filipinos as one block. The block and the 4 Americans make 5 units around the table: (5-1)!=24 ways. The Filipinos can be ordered inside the block in 3!=6 ways. Total =24×6=144.

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