A fan of country music plans to make a custom CD with 14 of her 25 favorite
songs. How many different combinations of 14 songs are possible?
25 songs, Choose 14 =
25C14 =
Since 14 is more than half of 25, we can subtract 14 from 25 and get 11.
That is,
25C14
can be simplified to
25C11
[That's because every time we choose 14 songs from the 25 to use, we choose 11
songs to leave out.]
25 Choose 11 = 25C11 = 
The factors on the bottom will all cancel into the factors on the top,
and after multiplying the remaining factors we end up with 4457400.
Edewin
