Question

A tv station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all the horror movies will be aired last (after all the science fiction movies). In how many ways can the station air the movie marathon?

Answer 1

Given:

Number of total movies = 11

Number of science fiction movie = 6

Number of horror movie = 5

Computation:

Number of science fiction movies way air = 6!

`\begin{gathered} =\text{ 6}*5*4*3*2*1 \\ =\text{ 720} \end{gathered}`

Number of horror movies way air = 5!

`\begin{gathered} =\text{ 5}*4*3*2*1 \\ =\text{ 120} \end{gathered}`

The number of ways the station air the movie marathon

`\begin{gathered} =\text{ 720 }*\text{ 120} \\ =\text{ 86400 ways} \end{gathered}`

Final answer

86400 ways