Question 387987: You have 8 posters to hang in your room. You want to hang the posters as a border around the walls of your room. How many ways can you arrange the posters?
a.40320
b.5040
c.720
d.362880
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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