Question

What’s the number of unique ways that angel can pick and arrange songs for the playlist.

Answer 1

It is given that 10 out of 12 songs need to be selected first and then arranged in a playlist.

The permutation can be used for the arrangements.

The formula for permutation is:

`_nP_r=(n!)/((n-r)!)`

Here n is the total number of things and r is the total number of selections.

In this problem n=12, r=10 so the total number of arrangements is given by:

`\begin{gathered} _(12)P_(10)=(12!)/((12-10)!) \\ =(12!)/(2!) \\ =239500800 \end{gathered}`

Hence the total number of arrangements that can be made is 239500800.