Question

DJ Davon is making a playlist for an internet radio show; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 15 rock, 20 blues, and 15 disco songs, and he wants to play an equal number of rock, blues, and disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

As we are playing a total of 12 songs here, the total number of ways to play 4 rock, 4 bues and 4 disco snogs is computed here as:

= Number of ways to select 4 rock songs from 15 rock songs * Number of ways to select 4 blues from 20 blues * Number of ways to select 4 disco songs from 15 disco songs * Number of permutation of 12 songs selected

$= \binom{15}{4}\binom{20}{4}\binom{15}{4}*20! = 2.20 \ \ X \ \ 10^{28}$

This is the total number of ways in which the playlist could be made here.