Answer:
[tex]C(10,4)=10C_4=210[/tex]
Step-by-step explanation:
A combination is an arrangement where the order is not important. Mathematically, a combination is the number of different groups of "[tex]n[/tex]" elements that can be formed from an initial group of "[tex]k[/tex]" elements. It's calculated with the following formula:
[tex]C(n,k)=nC_k=\frac{n!}{k!(n-k)!}[/tex]
Where:
[tex]k\leqslant n[/tex]
In this case:
[tex]n=10\\k=4[/tex]
Therefore the number of ways that the disc jockey selction can be done is:
[tex]C(10,4)=10C_4=\frac{10!}{4!(10-4)!} =\frac{10!}{4!(6!)}=210[/tex]
