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:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
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:
[tex]\begin{gathered} _{12}P_{10}=\frac{12!}{(12-10)!} \\ =\frac{12!}{2!} \\ =239500800 \end{gathered}[/tex]
Hence the total number of arrangements that can be made is 239500800.
