Question

A television programmer is arranging the order that five movies will be seen between the hours of 6 P.M. and 4 A.M. Two of the movies have a G​ rating, and they are to be shown in the first two time blocks. 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. until 4 A.M. Given these​ restrictions, in how many ways can the five movies be arranged during the indicated time​ blocks?

Answer 1

There are 4 different ways to arrange the five movies given the rating restrictions and assuming all movies are distinguishable.

Step-by-step explanation:

The subject question involves determining the number of ways to arrange five movies with given movie rating restrictions. With two movies having a G-rating to be shown in the first two time blocks and one NC-17 movie shown in the last time block from 2 A.M. to 4 A.M., we need to calculate the permutations of the remaining two time blocks for two movies.

Since the first two movies are G-rated and their order matters, there are 2! (2 factorial) ways to arrange them. The NC-17 movie has a fixed position in the last time block. Therefore, only the two time blocks in the middle can have their movies arranged in order, which gives us another 2!. In total, the number of arrangements is calculated as:

2! × 2! = 2 × 1 × 2 × 1 = 4 ways.

This is under the assumption that the two G-rated movies are distinguishable from each other, and so are the two movies for the middle time blocks. If they were not distinguishable, the number of arrangements would be different.