Question

A fan of country music plans to make a custom cd with 1313 of her 2525 favorite songs. how many different combinations of 1313 songs are​ possible? is it practical to make a different cd for each possible​ combination? how many different combinations of 1313 songs are​ possible?

Answer 1

This is asking how many ways can we choose 13 songs from a set of 25.
The formula is:
n! / r! * (n -r)!    =

25! / 13! * 12! which equals

25 *24 *23 *22 *21 *20 *19 *18 *17 *16 *15 *14 *13!  divided by
13! * 12! which equals

25 *24 *23 *22 *21 *20 *19 *18 *17 *16 *15 *14 divided by
12* 11* 10* 9* 8* 7* 6* 5* 4* 3* 2*

which equals

2,490,952,020,480,000 divided by 479,001,600

and that equals
5,200,300 combinations

Here's a combination calculator to check your work:
http://www.1728.org/combinat.htm