Question

2.  A committee of four people is to be formed from a set of six superheroes, seven supervillains, and four ordinary citizens. How many ways are there to form the committee if:

(a) Captain Marvel (a superhero), must be on the committee.

(b) At least two ordinary citizens must be on the committee.

(c) At most one supervillain can be on the committee.

(d) At least one superhero and one supervillain must be on the committee, but Mr. Fantastic (a superhero) and Dr. Doom (a supervillain) cannot be on the committee together.

(e) Neither Bruce Allen nor Peter Kent (ordinary citizens) can be on the committee if either Barry Parker or Clark Wayne (also ordinary citizens) are on it.

Hint: note that these are all four of the ordinary citizens.

Answer 1