Circular Permutation Practice Test

1. In how many ways can 6 people be seated at a round table?

• 120

• 140

• 180

• 60

Answer explanation

As discussed in the lesson, the number of ways will be (6 – 1)! therefore 5! = 120

2. How many different arrangements of 8 balls are possible in a circle, given that the clockwise and anticlockwise arrangements are different?

• 6090

• 5040

• 720

• 64

Answer explanation

Pn = (8-1)!

Pn = 7!

Pn = 5040

3. What is the Formula if the clockwise and anti-clockwise orders are different?

• n!

• (n-1)

• (n-1)! / 2!

• (n-1)!

Answer explanation

If clockwise and anticlockwise arrangements are the same, then we use the following formula to calculate the permutations:

Pn = (n-1)!

Here:

Pn = means circular permutation

n represents the number of objects in a set

4. How many different arrangements of 10 balls are possible in a circle given that the clockwise and anticlockwise arrangements are different?

• 362880

• 3991680

• 40320

• 5040

Answer explanation

Pn = (n-1)!

Pn = (10-9)!

Pn = 9!

Pn = 362880

5. How many different arrangements of 5 students are possible in a circle,  given that the clockwise and anticlockwise arrangements are the same?

• 24

• 120

• 12

• 2

Answer explanation

Pn = (n-1)! / 2!

Pn = (5 - 1)! / 2!

Pn = 4! / 2!

Pn = 24 / 2 = 12