\( 1 \leftarrow \) A DJ is preparing a playlist of 21 songs. How many different ways can the DJ arrange the first five songs on the playlist? There are \( \square \) different ways that the DJ can arrange the first five songs on the playlist. (Type a whole number.)

To find the number of different ways the DJ can arrange the first five songs from a playlist of 21 songs, you can use the concept of permutations. Since the order matters, you're looking to arrange 5 songs out of 21. The number of ways to arrange \( r \) items from \( n \) items is given by the formula: \[ P(n, r) = \frac{n!}{(n-r)!} \] In this case, \( n = 21 \) and \( r = 5 \): \[ P(21, 5) = \frac{21!}{(21-5)!} = \frac{21!}{16!} \] Calculating that gives: \[ = 21 \times 20 \times 19 \times 18 \times 17 = 21,628,320 \] So, there are \( \boxed{2163820} \) different ways that the DJ can arrange the first five songs on the playlist.