Question

20. How many ways can we select three door prizes from ten different ones (meaning each prize is unique) and distribute them among three people?

Answer 1

Selecting three door prizes from ten different ones, we have

$P^{10}_3=\text{ }\frac{10!}{(10-3)!}=\frac{10!}{7!}=\frac{10\times9\times8\times7!}{7!}=720$