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26 Jul 2003, 04:21
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What is the best approach here? I tryed the venn diagram, but it did not help.
Q.
Each of three charities in East Side 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?
Q.
Each of three charities in East Side 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?
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26 Jul 2003, 04:44
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employ a Venn diagram
A=8
B=8
C=8
ABC=4
if each pair of charities has 5 person in common, then this number includes those who serve in all the charities. Therefore, the number of people who serve in EXACTLY 2 charities is 1.
AB=1
BC=1
AC=1
N=8+8+8-1-1-1-2*4=13
A=8
B=8
C=8
ABC=4
if each pair of charities has 5 person in common, then this number includes those who serve in all the charities. Therefore, the number of people who serve in EXACTLY 2 charities is 1.
AB=1
BC=1
AC=1
N=8+8+8-1-1-1-2*4=13
26 Jul 2003, 04:52
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Thanks, Stolyar.
I wrongly assumed the meaning of "each pair of charities has five persons in common" as 5 persons serving in each pair only and was stuck because the total number appeared negative.
I wrongly assumed the meaning of "each pair of charities has five persons in common" as 5 persons serving in each pair only and was stuck because the total number appeared negative.
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