Question

DJ Raven is making a playlist for a website; she is trying to decide what 66 songs to play and in what order they should be played. If she has her choices narrowed down to 1111 country, 1616 rock, and 1919 blues songs, and she wants to play an equal number of country, rock, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Number of songs to be played = 6

Number of country songs = 11

Number of rock songs = 16

Number of blues songs = 19

She wants equal number of country, rock and blues songs, meaning she want 2 of each.

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of ways to select 2 country songs from 11 = 11C2 = 55

Number of ways to select 2 rock songs from 16 = 16C2 = 120

Number of ways to select 2 blues songs from 19 = 19C2 = 171

Total number of songs selections = 55 x 120 x 171 = 1,128,600

Number of possible arrangements of 6 songs = 6!

Number of playlists possible = 1,128,600 x 6!

= 8.13x10⁸