Answer: 2405970 ways
Step-by-step 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 :-
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : There are 135 people and three door prizes .
i.e. n= 135 , r= 3
Then, the total number of ways = [tex]^{135}P_3=\dfrac{135!}{(135-3)!}[/tex]
[tex]=\dfrac{135\times134\times133\times132!}{132!}\\\\=135\times134\times133\\\\=2405970[/tex]
Hence, there are 2405970 ways to distribute door prizes of $7,500, $750 and $75 .
