A television programmer is arranging the order that seven movies will be seen between the hours of 6 P.M. and \( 8 \mathrm{~A} . \mathrm{M} \). 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 0 of 1 of the time blocks, from 6 A.M. until 8 A.M. Given these restrictions, in how many ways can the seven movies be arranged during the indicated time blocks? The number of different ways the seven movies can be arranged during the indicated time blocks is \( \square \). (Type a whole number.)

To solve the problem, we follow these steps: 1. **Positioning the G-rated Movies:** We need to show the 2 G-rated movies in the first two time blocks. There are \(2!\) (or 2) ways to arrange them in these two blocks. 2. **Positioning the NC-17 Movie:** We need to place the NC-17 movie in the last time block (the last 0 of 1). Since its position is fixed, there are \(1\) way to place it. 3. **Positioning the Remaining Movies:** There are 4 remaining movies (7 total - 2 G-rated - 1 NC-17 = 4 remaining). We need to arrange these 4 movies into the remaining 4 time blocks. This can be arranged in \(4!\) (or 24) different ways. 4. **Calculating Total Arrangements:** To find the total arrangements, we multiply the number of arrangements at each step: \[ \text{Total arrangements} = 2! \times 1 \times 4! = 2 \times 1 \times 24 = 48 \] So, the number of different ways the seven movies can be arranged during the indicated time blocks is \( \boxed{48} \).