A music lover has 28 songs and is able to make a playlist of 12 songs (order doesn't matter). How many different 12-song playlists can be made? Is it realistic and practical to make all of them?

1 Answer

30,421,755 CDs. Realistic to make a CD of every combination? No. Practical? What is practicality to a true music lover?!?!?!


We have 28 songs and we're going to find how many ways we can put sets of 12 songs onto CDs. Since order doesn't matter (having songs 1 - 12 on a CD is the same as having songs 12 - 1 on the CD), we'll use the Combination calculation, which is:

#C_(28, 12)=(28!)/((12!)(28-12)!)=(28!)/((12!)(16!)#

And now let's evaluate this fraction:



There's a lot of cancelations, so I'll use colours to help keep track:


Let's clean this up and do one more round... I'm going to express 26 as #13xx2#



(To avoid the long and involved calculations, you can use the Combination calculator tool here: http://www.calculatorsoup.com/calculators/discretemathematics/combinations.php)