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

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 :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Given : There are 135 people and three door prizes .

i.e. n= 135 , r= 3

Then, the total number of ways = $^{135}P_3=\dfrac{135!}{(135-3)!}$

$=\dfrac{135\times134\times133\times132!}{132!}\\\\=135\times134\times133\\\\=2405970$

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