How many how many different ways can 8 people be arranged in a line...?

[Ladybugg50]

Hello, can you help me with this math problem? How many how many different ways can 8 people be arranged ina line without them being placed in the same order more than once.

 

[soroban]

Hello, !

I assume that you haven't learned Permutations.

How many different ways can 8 people be arranged in a line?

There are 8 choices for the 1st person;
there are 7 choices for the 2nd person;
there are 6 choices for the 3rd person;
there are 5 choices for the 4th person;
. . . and so on.

The number is: .\(\displaystyle 8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 \:=\:40,\!320\)

 

[Ladybugg50]

Hello Soroban, Thank you for your help. I'm just learning Permutations.

Hello, !

I assume that you haven't learned Permutations.


There are 8 choices for the 1st person;
there are 7 choices for the 2nd person;
there are 6 choices for the 3rd person;
there are 5 choices for the 4th person;
. . . and so on.

The number is: .\(\displaystyle 8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 \:=\:40,\!320\)