Question

Seven movies (A, B, C, D, E, F, and G) are being scheduled for a showing. The order of showing is determined by random selection. Find the probability that film C will be shown first, film A next-to-last, and film E last.

Answer 1

whats the formula? and which numbers go where?

Answer 2

there are a couple of ways to do this

Answer 3

number of ways to arrange all these 7 letters is
\[7!\]

Answer 4

you want to know how are favorable, that is, how many look like
C, _ , _ , _ , _ , A, E

Answer 5

you have 4 open slots to fill with 4 letters, and the number of ways you can do that is \(4!\)

Answer 6

1/7

Answer 7

so one method is to compute (if i am not mistaken) \(\frac{4!}{7!}\)
now we can try it another way

Answer 8

perfect

Answer 9

probability that C is first is
\[\frac{1}{7}\] then the probability that the second is not A or E is
\[\frac{4}{6}\]
the probability the next is not A or E is
\[\frac{3}{5}\] then
\[\frac{2}{4}\] then
\[\frac{1}{3}\] finally the probability the next is A is
\[\frac{1}{2}\] and these all must occur, so you can multiply them together and see if we get the same answer

Answer 10

we did. i just needed to get down to 1/210

Answer 11

yes, it is the same answer either method

Answer 12

another way to do it

there is only one way to pick slots 1, 6 and 7 to be C, A, and E respectively

this is out of 7 P 3 = (7!)/((7-3)!) = 210 ways total to pick 3 movies (for slots 1, 6 and 7)

So the probability is 1/210

Answer 13

this trick works because you don't need to worry about the ordering of the 4 slots (2 through 6)

Answer 14

nice

Answer 15

and much snappier i would say
it is good to see there is more than one way to skin a cat

Answer 16

Three lessons in one.

Answer 17

oops meant to say the 4 slots 2 through 5, but you get the idea

Answer 18

yeah i got the idea
didn't think of it this way