Question

A band has 7 new songs and wants to put 5 of them on a demo cd. how many different arrangements of 5 songs are possible.

Answer 1

Actually, this question first involves COMBINATIONS and then PERMUTATIONS.

We first must calculate how many combinations can 5 things can be chosen from 7.
The formula is:
n! / r! *(n -r)! =
7! / 5! * 2! =
7 * 6 * 5! / 5 ! * 2 =
7 * 6 / 2 = 21 ways we can choose 5 things from 7 objects.

Now we must see how many permutations there are of 5 things:
5 * 4 * 3 * 2 * 1 =
120

That means we can put each of the 5 song combinations into 120 "5 song sequences". 
So, the total number of ways is
21 * 120 = 2,520 possible ways.