Question 1125989
<font color="black" face="times" size="3">
Movies B, G and E are locked in slots 2, 7 and 8 respectively. So we have these movies left over to pick from: {A, C, D, F, H} which is a list of 5 items. 


For slot 1, we have 5 choices to pick from
Slot 2 is locked with movie B
For slot 3, we have 4 choices to pick from (we can't have a movie play twice)
For slot 4, we have 3 choices to pick from
For slot 5, we have 2 choices to pick from
For slot 6, we have 1 choice to pick from
Slot 7 is locked with movie G
Slot 8 is locked with movie E


Multiply out the values mentioned above: 5*4*3*2*1 = 120, which is the as writing 5! or 5 factorial.


So there are 120 different ways to arrange 5 items. By extension, there are 120 ways to arrange the five films in those slots mentioned above, while keeping slots 2, 7 & 8 locked.


This is out of 8! = 8*7*6*5*4*3*2*1 = 40,320 different ways to watch the eight movies in any order you want (not locking any of the slots). 


Divide the factorial values: 
(5!)/(8!) = (5!)/(8*7*6*5!) = 1/(8*7*6) = 1/336


The answer as a fraction is 1/336
In decimal form, that answer is approximately 0.002976
</font>