Call the 3 people A B and C and see how many possibilitys you get
A B C
A C B
B A C
B C A
C A B
C B A
What i do is slowly swap them so if you had 4 youde keep the first 2 the same
A B C D
A B D C
Then swap the second one
A C B D
A C D B
then swap again
A D B C
A D C B
and once they are all done, swap the first one and repeat (swap a to b, then swap the last 2 etc)