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?
A.
B.
C.
D.
E. Choose the correct choice from the following choices:
A) 8 B) 13 C) 16 D) 24 E) 27
Each group has 8 = 8+8+8= 
<gadget id="calculator">8+8+8</gadget>
<output>24</output>
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:13
<result>B</result>
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?
A.
B.
C.
D.
E.