Question

Question Help A television programmer is arranging the order that five movies will be seen between the hours of 6 P.M. and 4 A.M. One of the movies has a G​ rating, and it is to be shown in the first time block. One of the movies is rated​ NC-17, and it is to be shown in the last of the time​ blocks, from 2 A.M.A.M. until 4 A.M. Given these​ restrictions, in how many ways can the five movies be arranged during the indicated time​ blocks?

Answer 1

During the indicated time block of 6 PM-4 AM, the movies should go as follows: Since the G rating movies needs to be shown during the first time block, it would be first at 6 pm until around 8 pm. The NC-17 movie would also need to be LAST and from 2 am to 4 am. That leaves 3 movies left to be shown from around 8 pm to 2 Am, which could be shown in 6 different ways. If we assigned EACH movie a title of A, B or C, you get these different showing possibilities- ABC, ACB, BAC, BCA, CAB, and CBA. Since the first and last movies never change, they would default to the first and last positions while the rest is filled in.