I have uploaded the questions for you.you have to answer them all and show your work for each question and be clear about it

Every sample of size 6 has equal chance (randomly choose 6 students out of 30). Answer following questions: (a) How many possible samples?(b) p(s) = ?(c) ns = ?(d) Number of sample containing unit k?(e) First order inclusion probabilities?(f) Second order inclusion probabilitiesIf the design has a fixed sample size n, then pi ik> pi i +pi k -1 Give a brief example of surveys with the following properties. You should identify and define enough of the population, sampling frame, sample design and data collection to be convinving in your answers. The survey is not a probability sample. The survey is a probability sample but does not have a measurable design AND is not a systematic sample (SY). The survey is a probability sample with a measuable design, but there is likely to be a problem with some other aspect of the survey (e.g., non response or response error).The survey has a great design, but is simply impractical due to cost and/or time constraints.4. 2.6 from SSW (Särndal, Swensson, Wretman) 5. using the given data to running R code As an exercise, we will estimate the population of Iowa in the year 2000 based on a sample of counties.