Respuesta :
Answer:
The prizes can be awarded in 35904 ways.
Step-by-step explanation:
The order is important.
For example, John winning prize A, Laura prize B and Jonathan prize C is a different outcome than Laura winning prize A, John winning prize B and Jonathan winning prize C.
So we use the permutations formula to solve this problem:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!)}[/tex]
In how many ways can the prizes be awarded?
Three prizes divided among 34 contestants. So
[tex]P_{(34,3)} = \frac{34!}{(34-3)!} = \frac{34!}{31!} = 35904[/tex]
The prizes can be awarded in 35904 ways.
