Question

DJ Lorraine is making a playlist for a radio show; 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 19 rock, 14 pop, and 21 blues songs, and she wants to play an equal number of rock, pop, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Since D J Lorraine wants to play 15 songs in any order.

Given she has narrowed down

19 Rock

14 Pop

21 Blues song

And it is given that she wants to play equal number of songs from each genere

Therefore , she must select 5 songs from each given that total should be 15.

Number of ways of selecting songs =

Number of ways of playing these 15 songs = 15!

Therefore the total number of playlist that can be created =

Answer =