Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?\nA.\nB.\nC.\nD.\nE.\nOptions:\n(A) 8\n(B) 13\n(C) 16\n(D) 24\n(E) 27 Stream of consciousness first, then make a decision:
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Each group has 8 = 8+8+8 = 24 max\n4 people are in 2 groups, subtract 4 people twice as they are counted twice\nEach pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group\nAns: 8+8+8-(2(4)) - 3 = 13
Thus, the answer is (B).
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