Question

There are 8 movies you would like to see currently showing in theaters.
A) In how many different ways can you see all 8 movies?
B) In how many ways can you choose a movie it see this friday and one to see this Saturday?

Answer 1

Presumably, the order matters. Otherwise there would only be one way to view them. From \(8\) movies, you're viewing all \(8\) in some sequence, which can be computed as
\[8!\binom88=8!{}_8C_{8}={}_8P_8=\frac{8!}{(8-8)!}\]
For the second question, assuming you don't want the same movie twice, you're only viewing \(2\) of the \(8\), which means you can compute the number of ways by
\[2!\binom82=2!{}_8C_{2}={}_8P_2=\frac{8!}{(8-2)!}\]