Answer: The possible ways are [tex]1.07\times 10^{16}[/tex]
Step-by-step explanation:
Since we have given that
Number of songs to play = 14
Number of hip hop = 7
Number of jazz song = 5
Number of pop song = 7
Number of blues song = 8
Total songs = [tex]7+5+7+8=27[/tex]
Number of songs with hip hop = 27 - 7 =20
So, Number of ways to play no more than 3 hip hop songs is given by
[tex]^{20}P_{14}+^{20}P_{13}\times ^7P_1+^{20}P_{12}\times ^7P_2+^{20}P_{11}\times ^7P_3\\\\=1.07\times 10^{16}[/tex]
Hence, the possible ways are [tex]1.07\times 10^{16}[/tex]