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board of directors

by mehrasa » Wed Sep 28, 2011 12:08 am
each of three charities 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?
1) 8
2) 13
3) 16
4) 24
5) 27
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by shankar.ashwin » Wed Sep 28, 2011 12:28 am
You could do this using venn diagrams, i am lazy to draw so directly using formula for 3 sets;

Let A,B and C be 3 boards.

n(total) = n(A) + n(B) + n(C) - N(AB) -n(AC) - n(BC) + N(ABC)
= 8+8+8-5-5-5+4 = 13
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by mehrasa » Wed Sep 28, 2011 5:35 am
ya, the answer is correct...
i have a Q no. i know this formula
when sets have over lapping:
total= G1+G2+G3+N-B-T(2)
N: none
B: both
and T: three

why you add n(ABC).. Do we have to always add this number?
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by shankar.ashwin » Wed Sep 28, 2011 5:46 am
Refer this, useful for any set theory problem

https://www.beatthegmat.com/mba/2011/01/ ... set-theory
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