Question

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

Answer 1

Since five door prizes are to be selected from eight different ones, we have

`C^{8_{}}_5`

Recall that

`C^n_r=(n!)/((n-r)!r!)`

Thus,

`C^{8_{}}_5=(8!)/((8-5)!5!)=(8!)/(3!*5!)`

This gives

`(8*7*6*5!)/(3*2*1*5!)=56`

To be distributed among five people results to

`P^(56)_5=\text{ }(56!)/((56-5)!)=458377920`