Question

Over the next week you want to watch a movie a day. In how many ways can this be done if you have 8 movies?

A.

56

B.

6,720

C.

40,320

D.

2,097,152

​

Answer 1

40,320

Explanation:

First you have 8 movies to watch.

A day passes you have 7 left, then another day passes you have 6 left...

You do this until you have 1 movie left because by then you'd have watched 7 movies in 7 days of a week.

Take the product: 8 * 7 * 6 * 5...*2*1 = 8! = 40,320

Answer 2

Answer: C. 40,320

Explanation:

Given : The total number of movies = 8

Also, in one week if you watch one movie a day , then the number of possible movies you can watch in next week must be 7.

Now, the number of ways to watch 8 movies taking 7 movies from is given by permutations :-

`^8P_7=(8!)/((8-7)!)\\\\=(8!)/(1!)=8*7*6*5*4*3*2*1\\\\=40,320`