each of 3 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 ? a . b . c . d . e .	Choose the correct choice.
A) 8  B) 13  C) 16  D) 24  E) 27

Rationale: each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b
Answer: B