DJ Howard is making a playlist for a radio show; he is trying to decide what songs to play and in what order they should be played.
If he has his choices narrowed down to reggae, pop, and rock songs, and he wants to play an equal number of reggae, pop, and rock songs, how many different playlists are possible?

The number of different playlists possible with order important = 1.9996 × 10¹³ ways = 2.00 × 10¹³ ways

Step-by-step explanation:

Selection problems in which the order matters are permutation problems.

So, the choices are 4 reggae songs from 11

4 pop songs from 12

4 rock songs from 23

number of ways = ¹¹P₄ × ¹²P₄ × ²³P₄ = 7920 × 11880 × 212520 = 19,995,921,792,000 = 1.9996 × 10¹³ ways