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

You can select from any of the 8 on the first day, leaving 7 to choose from on the second day, leaving 6 for the third. So, 8 x 7 x 6 x 5 x 4 x 3 x 2 or 8! That's 8factorial, so multiply those out or use a calculator to get 8! and that is your answer.