# Question on Set Theory

The problem statement is: "It was found that out of 100 consumers, foll. are the details of preference for 3 brands A,B and C.

(a) Brand A - 50 consumers

(b) Brand B - 40 consumers

(c) Brand C - 30 consumers

(d) Both brands A and B - 20 consumers

(e) Both brands B and C - 15 consumers

(f) Both brands A and C - 10 consumers

Find how many used all the 3 brands A, B and C?"

I used the formula (x = intersection):

n(AUBUC) = n(A) + n(B) + n(C) - n(AxB) - n(AxC) - n(BxC) + n(AxBxC)

=> 100 = 50+40+30-20-15-10+n(AxBxC)

=> n(AxBxC) = 25

Somehow, I am not convinced that the answer is correct, one of the reasons being n(AxBxC) is > n(AxB), n(AxC), n(BxC).

Can you pl. clarify/confirm if my approach and answer are correct?