Tim, Fred, Margory, and Amy are playing a game. In how many different orders Could they each play their turn?

Question

Tim, Fred, Margory, and Amy are playing a game. In how many different orders could they each play their turn?

Answer 1

Imagine there are 4 places and 4 people

 

____, ____, _____, _____

 

The 1st place can be filled in 4 ways ----- 1st place is filled

The 2nd place can be filled in 3 ways , as one person already occupies the 1st place ---- now 2nd place is filled

The 3rd place can be filled in 2 ways, as two persons have already filled the 1st two places ---- now 3rd place is filled

The last place can be filled in 1 way as only one person is remaining

 

Therefore, number of ways 4 people can play their game = 4 * 3 * 2 * 1 = 24 ways = 4!

Answer 2

The first player could be chosen in 4 ways --- the second player could then be chosen in 3 ways --- the third player could then be chosen in 2 ways --- the fourth player could then be chosen in one way only --- the total number of ways (different orderings) that these four players could be chosen would then be 4! = 4(3)(2)(1) = 24