Discuss the below:
The Republican governor of a state with no income tax is appointing a committee of five members to consider changes in the income tax law. There are 15 state representatives--seven Democrats and eight Republicans--available for appointment to the committee.
Q: Assume that the governor selects the committee of five members randomly from the 15 representatives.
a- In how many different ways can the committee members be selected?
b- What is the probability that no Democrats is appointed to the committee? If this were to occur, what would you conclude about the assumption that the appointments were made at random? Why?
c- What is the probability that the majority of the committee members are Republicans? If this were to occur would you have reason to doubt the governor made the selections randomly? Why?