A coach is choosing 4 students to go to a badminton competition (the order of selection does not matter). There are 20 and 15 girls to choose from, and the coach chooses randomly so everyone an equal chance of being picked, but nobody can be picked more than once.
a. What is the probability that all 4 chosen will be boys?
b. What is the probability that all 4 chosen will be girls?
c. Should these two probabilities add up to 1? Why or why not?