Question

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.

Answer 1

Answer: 7.94 x 10^17

Explanation:

Answer 2

Answer: The possible ways are
`1.07* 10^(16)`

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 =
`7+5+7+8=27`

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

`^(20)P_(14)+^(20)P_(13)* ^7P_1+^(20)P_(12)* ^7P_2+^(20)P_(11)* ^7P_3\\\\=1.07* 10^(16)`

Hence, the possible ways are
`1.07* 10^(16)`