Chris has 25 songs in his library and wants to put 12 of them into a playlist. If he picks songs at random, how many different groups of songs can be created?

1 Answer

#5,200,300# different playlists (and at this point we're only grouping songs - we aren't even playing with different ordering of playlists!)


We're working with a combination, which means a playlist that includes songs A and B, no matter the order, are the same (a permutation, on the other hand, counts playlists with different song orders as different).

The general equation for a combination is:

#C_(n,k)=(n!)/((k)!(n-k)!)# with #n="population", k="picks"#


There are two ways to evaluate this - we can choose to go the multiplication route:


and work through that cancellation nightmare (but do-able on a simple calculator), or we can recognize that factorials are really just numbers (ex. 3! = 6, 4! = 24, etc) and so substitute in using a factorial table:


Since my calculator doesn't stand a chance of working this through, I'll copy and paste into google calculator:

and we get #5,200,300#