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? Express your answer in scientific notation rounding to the hundredths place

Answer 1

4.4 * 10^21

Explanation:

Given :

Number of pop, n(p) = 10

Number of reggae, n(r) = 25

Number of blues, n(b) = 10

Total number of songs to select (n) = 15

If she wants equal Number if the 3 genres

Each genre will have : 15/3 = 5 songs each

Hence,

(10C5 * 25C5 * 10C5) * n!

Combination formula :

pCr = p! / (p-r)! r!

Using calculator to save computation time :

(10C5 * 25C5 * 10C5) * n!

(252 * 53130 * 252) * 15!

= 4412050844368527360000

= 4.4 * 10^21