Question

DJ Ali is making a playlist for a friend; she is trying to decide what 99 songs to play and in what order they should be played. If she has her choices narrowed down to 1616 blues, 2323 country, and 1515 jazz songs, and she wants to play an equal number of blues, country, and jazz songs, how many different playlists are possible

Answer 1

If she wanted to play 99 songs and play an equal amount of blues, country, and jazz she would play 33 songs from each category.

33 blues

33 country

33 jazz

= 99 songs

Explanation:

Answer 2

Answer: 1.637 x 10¹⁴ different playlists

Step-by-step explanation: Since DJ Ali needs to choose 9 songs and wishes that the number of blues, country and jazz songs are the same, she needs to pick 3 songs of each type. The total number of ways she can choose the songs, without considering their order is:

The number of possible ways of ordering those nine song is:

There are 1.637 x 10¹⁴ different possible playlist.