A) The sovereign has to choose a prime minister among 6 candidates and a court jester among 5 candidates. Thankfully, nobody is a candidate in both lists. How many possible pairs of prime minister and jester can be appointed?

b) This time, the sovereign has to choose both a minister of education and a minister of environment, both from the same list of 6 candidates. How many possible pairs of ministers can be appointed?

c) Finally, the sovereign has to choose 2 justices of the supreme court, both from a list of 6 candidates. How many possible pairs of justices can be appointed? [Note that in this case the 2 positions to fill are indistinguishable, therefore the ordering of the elected justices........]