Circular Permutations

Quiz

circular permutations

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1/3

How many ways are there to seat 4 individuals around a circular table?

Option C 4! / 3! ways

Option B (4-1)! ways

Option A 4! ways

right answer

We arrange n objects around a circle in (n-1)! = n!/n ways Thus to arrange 4 individuals around a circle, we have (4-1)! ways

2/3

There are 10 colleagues sitting at a round table. There are 2 females and 8 males. How many ways are there to seat them such that the 2 females have to sit together?

Option C 2! x (8-1)!

Option B 2! x (10-1)!

Option A 2! x (9-1)!

right answer

(10 colleagues: 2 Females, 8 Males) Consider the 2 females as a single unit and arrange them within themselves: 2! ways Now arrange this female unit with the 8 males (total of 9 units) around the table: (9-1)! ways Thus number of ways to seat them such that the 2 females have to sit together: 2! x (9-1)! ways

3/3

A family of 6 with 4 adults and 2 children sits at a round dinner table. How many ways are there to sit them so that the 2 children are separated?

Option C 5! - (2! x3!)

Option B 5! - (2! x 4!)

Option A 2! x 4!

right answer

Consider number of ways to arrange the 6 members without restrictions: (6-1)! = 5! ways Consider when the 2 children are together as 1 unit then arrange this unit with the 4 other adults: 2! x (5-1)! = 2! x 4! ways Thus number of ways where 2 children are separated = 5! - (2! x 4!) (This is what we call the complementary method!) Think: Is there any alternative way to do this?

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