A scout troop is arranged in a circle for an opening ceremony. If there are 14 scouts, in how many unique ways can they stand around the circle?

Question

a) 196

b) 6 227 020 800

c) 479 001 600

d) 87 178 291 200

 

I put d, but the correct answer was b. Just want to know why.

Answer 1

There are (n−1)! ways to arrange n distinct objects in a circle (where the

clockwise and anti-clockwise arrangements are regarded as distinct.)

 

n=14

 

(n-1)! = 13! = 6,227,020,800

 

https://www.intmath.com/counting-probability/3-permutations.php

Loot at Theorem 4 on the above page