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What is the best approach here? I tryed the venn diagram, [#permalink]
26 Jul 2003, 03:21
What is the best approach here? I tryed the venn diagram, but it did not help.
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?
imagine three overlapping circles. you need to find an area of this construction. BUT!!! you cannot simply add areas of the given circles. some areas overlap twice and one thrice. you have to eliminate these pieces in order not to count them many times.
So, we have to eliminate 'double' regions, and 'triple' region. In doing so, we 'clear' our construction from any overlapping.
AREA=A+B+C-exactly AB-exactly AC-exactly BC-2*ABC
The problem is much complicated when it comes to deal with four and more overlapping sets.
Last edited by stolyar on 26 Jul 2003, 12:12, edited 1 time in total.