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

Explanation:

95060

Answer 2

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

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

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=(n!)/((n-m)!)`

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

`^(100)P_(3)=(100!)/((100-3)!)=(100!)/(97!)\\\\=100*98*97=950600`