Answer
There are 479,001,600 ways to arrange the songs.
Work Step by Step
1st song: 12 choices.
2nd song: 11 choices.
3rd song: 10 choices.
...
11th song: 2 choices.
12th song: 1 choice.
Using the Multiplication Rule of Counting (see page 298) with fatorial:
$12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1=12!=479,001,600$