Question

There are 135 people and three door prizes. how many ways can door prizes of $7,500, $750 and $75 be distributed?

Answer 1

Answer: 2405970 ways

Explanation:

When the order of selecting r individuals out of n individual , we use permutations.

The number of permutations of r things taking out of n things is given by :-

`^nP_r=(n!)/((n-r)!)`

Given : There are 135 people and three door prizes .

i.e. n= 135 , r= 3

Then, the total number of ways =
`^(135)P_3=(135!)/((135-3)!)`

`=(135*134*133*132!)/(132!)\\\\=135*134*133\\\\=2405970`

Hence, there are 2405970 ways to distribute door prizes of $7,500, $750 and $75 .