Answer:
1.637 x 10¹⁴ different playlists
Step-by-step explanation:
Since DJ Ali needs to choose 9 songs and wishes that the number of blues, country and jazz songs are the same, she needs to pick 3 songs of each type. The total number of ways she can choose the songs, without considering their order is:
[tex]N_{songs} =C(16,3)*C(23,3)*C(15,3)\\N_{songs} =\frac{16!}{(16-3)!3!}*\frac{23!}{(23-3)!3!}*\frac{15!}{(15-3)!3!}\\N_{songs} = 451,250,800[/tex]
The number of possible ways of ordering those nine song is:
[tex]N_{ways} = 451,250,800*P(9,9)\\N_{ways} = 451,250,800*\frac{9!}{(9-9)!}\\N_{ways} =1.637*10^{14}[/tex]
There are 1.637 x 10¹⁴ different possible playlist.
