dunkin77 wrote:Each of three charities in Novel Grove Estate 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 8
B 13
C 16
D 24
E 27

Can anyone help?

Is it 13?

4 people serve on all 3 boards - A, B and C

We are given that each pair of charities have 5 in common (of which
4 are already accounted for above). So,

1 person serves on A and B
1 person serves on B and C
1 person serves on A and C

Now, total number of unique persons = 4 + 3 = 7 and tally is as below -

A: 6
B: 6
C: 6

Since each board has 8 members, the other 2 members in each board
have to be unique.

So, total = 7 + 2 + 2 + 2 = 13

Thanks Jay for your help.

Yes - you are correct - the answer is 13.