Question

DJ Jacqueline is making a playlist for a friend; she is trying to decide what 15 songs to play and in what order they should be played. If she has her choices narrowed down to 10 pop, 25 reggae, and 10 blues songs, and she wants to play an equal number of pop, reggae, and blues songs, how many different playlists are possible

Answer 1

`P=4.41205084*10^2^1`

Explanation:

From the ques ton we are told that

Total amount N=15

Choices within 10 pop, 25 reggae, 10 blues

Generally for equal amount in her play list she's mathematically Going to have 5 of each kind Pop,Reggae,Blues

Therefore

Let the amount of differnt playlist be given as P

`P=^1^0C_5*^2^5C_5*^1^0C_5*15!`

`P=252*53130*252*1307674368000`

`P=4.41205084*10^2^1`

Therefore
`P=4.41205084*10^2^1` different playlists are possible