My class consists of 8 men and 7 women. I want to pick a group of 6 people for research. Write each answer using fraction as needed.

a. In how many different ways can I pick this group?

b. What is the probability of having exactly 3 men in the group?

c. What is the probability of all the selected people in the group are women?

d. What is the probability of having at least one man in the group?

Please explain step by step, no Excel!