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 :-

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

Part 1:
6(x-5) = 5(x+5) (x = 55)
4y + 2 (-3 + 2y) = 1-y (x = 7/9)
Part 2:
4(a-6) = 8a - (4a-24) (No Solution)
4(2x-8) = 8(x-8) (No Solution)
2(3x-3) = -6x-6 (Identity (x = 0))
Answer:
Explained below.
Step-by-step explanation:
The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4,502 employees at the company and wants to conduct a systematic sample of size 50.
Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and a static, periodic interval.
(a)
A sample of size 50.
Then the value of <em>k</em> will be: 
Thus, the value of <em>k</em> is 90.
(b)
Label the employees from 1 to 4502.
And select every 90th employee.
So, the individuals who will be administered the survey are:
90th, 180th, 270th,...
Explanation is in the file
tinyurl.com/wtjfavyw
The answer may be c but if not i am super sorry!!