Question

There are 125 people and three door prizes. How many ways can three door prizes of $50 each be distributed? How many ways can door prizes of $5,000, $500 and $50 be distributed?

Answer 1

We have been given that there are 125 people and three door prizes.

In the first part we need to figure out how many ways can three door prizes of $50 each be distributed?

Since there are total 125 people and there are three identical door prices, therefore, we need to use combinations for this part.

Hence, the required number of ways are:

$_{3}^{125}\textrm{C}=\frac{125!}{122!3!}=\frac{125*124*123}{1*2*3}=317750$

In the next part, we need to figure out how many ways can door prizes of $5,000, $500 and $50 be distributed?

Since we have total 125 people and there are three prices of different values, therefore, the required number of ways can be figured out by using permutations.

$_{3}^{125}\textrm{P}=\frac{125!}{122!}=125*124*123=1906500$