Question

A television programmer is arranging the order that six movies will be seen between the hours of 6 P.M. and 6 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 4 A.M. until 6 A.M. Given these restrictions, in how many ways can the six movies be arranged during the indicated time blocks?​

Answer 1

Let's break down the problem and solve it step by step.

1. The first two time blocks are reserved for G-rated movies. We have two G-rated movies that need to be arranged in these blocks. The number of ways to arrange them is 2! (2 factorial), which is equal to 2.

2. The last time block, from 4 A.M. until 6 A.M., is reserved for an NC-17 movie. So, we have only one choice for this block.

3. The remaining three time blocks are available for the remaining three movies. We have three movies left: two G-rated and one unknown rating. The number of ways to arrange three movies is 3! (3 factorial), which is equal to 6.

To find the total number of ways to arrange the six movies, we multiply the number of choices at each step:

Total number of arrangements = 2 (for the G-rated movies) * 1 (for the NC-17 movie) * 6 (for the remaining three movies)

Total number of arrangements = 2 * 1 * 6 = 12

Therefore, there are 12 different ways to arrange the six movies during the indicated time blocks.