Answer :
We need to find the number of combinations of 3 songs out of 15 songs.
The combination of r items out of a total of n items is given by the formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]where
[tex]n!=n(n-1)(n-2)...(2)(1)[/tex]In this problem, we have:
[tex]\begin{gathered} n=15 \\ r=3 \end{gathered}[/tex]Thus, we obtain:
[tex]\begin{gathered} C(15,3)=\frac{15!}{3!(15-3)!} \\ \\ C(15,3)=\frac{15\cdot14\cdot13(12!)}{3\cdot2\cdot1(12!)} \\ \\ C(15,3)=\frac{15}{3}\cdot\frac{14}{2}\cdot13 \\ \\ C(15,3)=5\cdot7\cdot13 \\ \\ C(15,3)=455 \end{gathered}[/tex]Answer: The number of ways they can choose their set of songs is 455.
