A student in Singapore wants to apply to a business school in Singapore. Suppose there are 5 private and 3 public business schools in the city. She wants to select two schools from each sector.

a. How many different choices can the student make?

b. One of the private schools and one of the public schools have underperformed. If the student selects the schools at random, what is the probability that at least one of the schools will underperform the next year?