Question

In the following​ exercise, does the problem involve permutations or​ combinations? Explain your answer. One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is​ $100, second prize is​ $50, and third prize is​ $25, in how many different ways can the prizes be​ awarded?

Answer 1

Answer: Permutation is involved , since order of prizes matters.

The number of different ways the prizes can be​ awarded =95060

Step-by-step explanation:

Given : Total number of people purchase lottery tickets =100

The number of prizes = 3

Since each prize can be claimed by only one person.

So order matters here, there for we use permutations .

The number of permutations of n objects taken m at a time is given by :-

$^nP_m=\dfrac{n!}{(n-m)!}$

Then, the number of different ways the prizes can be​ awarded :-

$^{100}P_{3}=\dfrac{100!}{(100-3)!}=\dfrac{100!}{97!}\\\\=100\times98\times97=950600$