Question

Toby got a summer job at a movie theater cleaning the aisles after each film. This Sunday, 8 movies are scheduled to show, 6 of which feature a teenager as the one main protagonist.If Toby is randomly assigned to clean up after 5 movies, what is the probability that all of them feature a teenager as the one main protagonist?Write your answer as a decimal rounded to four decimal places.

Answer 1

If Toby is randomly assigned to clean up after 5 movies, the probability that all of them feature a teenager as the one main protagonist is 0.0083

Explanation:

Since we don't care about the particular order of the movies, we have that the total possible number of combinations in which Toby cleans up after 5 movies that feature a teenager as the one main protagonist can be calculated using a combination, as following:

`8C5\rightarrow(8!)/((8-5)!5!)\rightarrow56`

Now, to find the total number of possible combinations for picking 5 movies out of the 8, we use a permutation, as following:

`8P5\rightarrow(8!)/((8-5)!)\rightarrow6720`

Therefore, If Toby is randomly assigned to clean up after 5 movies, the probability that all of them feature a teenager as the one main protagonist is:

`(56)/(6720)\rightarrow0.0083`