Questions: A TV station is going to air a movie marathon with 7 movies. It will consist of 5 science fiction movies and 2 horror movies. The horror movies will be aired later in the evening. So, both of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?

Solution Steps

The TV station is airing a movie marathon consisting of 7 movies: 5 science fiction movies and 2 horror movies. The horror movies must be aired last, after all the science fiction movies. We need to determine the number of ways the station can arrange the movie marathon under these constraints.

Since the horror movies must be aired last, we can treat the problem as two separate parts:

1. Arrange the 5 science fiction movies.
2. Arrange the 2 horror movies after the science fiction movies.

The number of ways to arrange 5 science fiction movies is given by the number of permutations of 5 items: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

The number of ways to arrange 2 horror movies is given by the number of permutations of 2 items: \[ 2! = 2 \times 1 = 2 \]

Since the arrangements of the science fiction movies and the horror movies are independent, the total number of ways to arrange the movie marathon is the product of the two permutations: \[ 5! \times 2! = 120 \times 2 = 240 \]

Final Answer