DJ Mykel is making a playlist for a radio show; he is trying to decide what 1414 songs to play and in what order they should be played. Step 1 of 2 : If he has his choices narrowed down to 77 hip-hop, 55 jazz, 77 pop, and 88 blues songs, and he wants to play no more than 33 hip-hop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Respuesta :

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]