Suppose you're helping to organize a summer sports camp, and the following problem comes up. The camp is supposed to have at least
one counselor who's skilled at each of the sports covered by the camp (baseball, volleyball, and so on). They have received job applications from potential counselors. For each of the sports, there is some subset of the applicants qualified in that sport. The question is: For a given number , is it possible to hire at most of the counselors and have at least one counselor qualified in each of the sports? We'll call this the Efficient Recruiting Problem.
Show that Efficient Recruiting is NP-complete.