Question 387987
I believe the answer is 8! which is equal to 8*7*6*5*4*3*2*1 which equals 40320.
If it were 3 posters, the answer would be 3! = 6
3! can be shown
8! is a lot more difficult to show.
We'll show 3!
Let the posters be a, b, and c.
The ways they can be shown are:
abc
acb
bac
bca
cab
cba
With 4 posters, the number of ways they can be shown is 4! = 24 possible ways.
Let the posters be a, b, c, and d
The ways they can be shown are:
abcd
abdc
acbd
acdb
adbc
adcb
bacd
badc
bcad
bcda
bdac
bdca
cabd
cadb
cbad
cbda
cdab
cdba
dabc
dacb
dbac
dbca
dcab
dcba

As the number of posters goes up, the number of possible permutations gets significntly higher.

The number you are looking for is 8! = 40320