3. [30 points Collaborative Problem: Suppose you\'re helping to organize a summe

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3. [30 points Collaborative Problem: 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 n sports covered by the camp (baseball, volleyball, and so on). They have received job applications from m potential counselors. For each of the n sports, there is some subset of the m applicants qualified in that sport. The question is "For a given number k m, is it possible to hire at most k of the counselors and have at least one counselor qualified in each of the n sports?" We'll call this the Eficient Recruiting Problem. Prove that Efficient Recruiting is NP-complete.

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