DJ Davon is making a playlist for work; 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 14 blues, 25 country, and 21 disco songs, and he wants to play an equal number of blues, country, and disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

If he has narrowed down his choices to 14blues, 25 country and 21 disco songs and he has to make a list of 12 songs with equal representation of each genre of song, the it means there will be 4 songs from each genre of music.

We select this 4 different songs using the combination formula for selection and multiply our results.

This means we have:

12C4 for blues,

25C4 for country

21C4 for disco.

This gives:

=12C4 * 25C4 * 21C4

= 495 * 12650 * 5985

And the order they can be played = 12!.

We then multiply the number of ways to get these songs by the order they can come in.

That is:

=495 * 12650 * 5985 * 12!

= 1.7951 * 10^19

= 1.80 * 10^19 (nearest hundredth).