A DJ is preparing a playlist of 17 songs. How many different ways can the DJ arrange the first four songs on the playlist? There are \( \square \) different ways that the DJ can arrange the first four songs on the playlist. (Type a whole number.)

We need to determine the number of different ways to arrange the first four songs out of 17. This is a permutation problem where order matters. 1. **Identify the problem type:** Since the order of the songs matters, we use permutations. 2. **Use the permutation formula:** The number of ways to arrange \( k \) items from \( n \) items is given by \[ P(n, k) = \frac{n!}{(n-k)!} \] Here, \( n = 17 \) and \( k = 4 \). 3. **Plug in the values:** \[ P(17, 4) = \frac{17!}{(17-4)!} = \frac{17!}{13!} \] 4. **Simplify the fraction:** Notice that \[ \frac{17!}{13!} = 17 \times 16 \times 15 \times 14. \] 5. **Calculate step-by-step:** \[ 17 \times 16 = 272, \] \[ 272 \times 15 = 4080, \] \[ 4080 \times 14 = 57120. \] Therefore, there are \( \boxed{57120} \) different ways that the DJ can arrange the first four songs on the playlist.