Answer:
1.80 * 10^19
Step-by-step explanation:
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).
