Number of actual directors "lost" Sets problem

I think the answer is 3

nope! this is not the answer!

Oops..I think the answer should be 2.

Oops..I think the answer should be 2.

figure for answer

answer is 13

Okay .. did i read it wrong? .. does the question mean that how many are distinct in total? then it is definitely 13.

i could'nt understand how are 13 people distinct. Please explain if you got it.

if you add all the numbers from the latest figure, 2+2+2+1+1+1+4 =13

i.e. there are 13 distint persons satisfying all the conditions and serving on the 3 boards:
condition 1. 4 serve on 3 boards each (lets say, board a, b and c)
condition 2. each pair i.e. ab, bc, ca has 5 in common, and we have 4 from condition 1. so we need 1 person common between each pair to make it total 5.
condition 3. since each board has 8 persons in total, hence there must be 2 persons on each board who work only on that board.

hence 13 different persons in total are serving on 3 boards under above conditions.

If we need to apply following equation here...how do we apply here??

For 3 sets A, B, and C: P(AuBuC) : P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

I am not able to understand how we can make use of this equation?

Thanks in advance for your reply and time..

raijonney wrote:if you add all the numbers from the latest figure, 2+2+2+1+1+1+4 =13
conditions.

In terms of :
P(AuBuC) : P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

P(A), P(B),P(C) is the number of people in each board i.e. 8
P(AnB), P(AnC), P(BnC) is intersection i.e. common person in 2 boards i.e. 5
P(AnBnC) is intersection of all boards, i.e. common person in all 3 boards i.e. 4

hence the equation will be => 8 + 8 + 8 - 5 - 5 - 5 + 4 = 13, hence the answer.