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?
Accepted Solution
A:
Answer: Permutation is involved , since order of prizes matters.The number of different ways the prizes can be awarded =95060Step-by-step explanation:Given : Total number of people purchase lottery tickets =100The number of prizes = 3Since 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 :-[tex]^nP_m=\dfrac{n!}{(n-m)!}[/tex]Then, the number of different ways the prizes can be awarded :-[tex]^{100}P_{3}=\dfrac{100!}{(100-3)!}=\dfrac{100!}{97!}\\\\=100\times98\times97=950600[/tex]