Circular Permutations

Circular permutations often pose some difficulty to students. Let’s consider the following scenarios:

Scenario A: 10 people to be seated at a round table with 10 identical seats

Number of ways = (10-1)! = 9! = 362880

Scenario B: 5 people to be seated at a round table with 10 numbered seats

Number of ways = 10 P 5 = 30240

Scenario C: 6 people to be seated at a round table with 10 identical seats

circular

There will be 4 identical empty seats. Consider fixing 1 occupied seat, and permutate the other 9 seats around it. There are 4 identical seats among the 9 seats. So number of ways = 9!/4! = 15120

1 thought on “Circular Permutations

  1. Hi, are you referring to scenario B, 5 people to be seated at a round table with 10 numbered seats?
    then you are right. it can also be calculated as simply 10 P 5. thanks 🙂

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