DJ Kenisha is making a playlist for a radio show; she is trying to decide what 6 songs to play and in what order they should be played. If she has her choices narrowed down to 5 reggae, 15 hip-hop, and 13 blues songs, and she wants to play an equal number of reggae, hip-hop, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

different playlists are possible

Step-by-step explanation:

The order in which the songs are played is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

6 songs, so 2 reggae(from a set of 5), 2 hip hop(from a set of 15) and 2 blues(from a set of 13). So

In scientific notations:

4 digits after the first, which is 8, so:

different playlists are possible

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50