Question 1125989: Eight Movies (A,B,C,D,E,F,G,& H) are being scheduled for showing. The order of showing. The order of showing is determined by random selection. Find the probability that film b will be shown first, film G next to last and film E last.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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
|
|
|
