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?
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27 OK. Let's think. Some random thoughts first:
user
A intersect B intersect C = 4
A intersect B but not C = 1
B intersect C but not A = 1
C intersec A but not B = 1
A only is 2; B only is 2; C only is 2
Therefore, total 13 members serve on one or more boards of directors. The answer: (B).
assistant