A school leadership team consists of 18 junior and senior students. Of the 10 students representing the senior class, 6 are female, and 4 are male. Of the 8 students representing the junior class, 3 are female, and 5 are male. a. In how many ways can a safety committee of 5 students be selected from the group?
b. In how many ways can a president, vice president, and treasurer be selected from the group if each person can only hold one position?
c. Given that a female from this group is going to be honored for an award, what is the probability that the female is a senior?
d. The junior class is planning a special “good bye” ceremony for the senior class and needs to select a diverse group of juniors for the task. In how many ways can they select 2 males and 2 females from the junior class for this special committee?
e. 4 juniors are being chosen for the special “good bye” ceremony committee. Find the probability that the selected committee consists of 2 males and 2 females.