Since five door prizes are to be selected from eight different ones, we have
[tex]C^{8_{}}_5[/tex]Recall that
[tex]C^n_r=\frac{n!}{(n-r)!r!}[/tex]Thus,
[tex]C^{8_{}}_5=\frac{8!}{(8-5)!5!}=\frac{8!}{3!\times5!}[/tex]This gives
[tex]\frac{8\times7\times6\times5!}{3\times2\times1\times5!}=56[/tex]To be distributed among five people results to
[tex]P^{56}_5=\text{ }\frac{56!}{(56-5)!}=458377920[/tex]
