Question

One hundred twenty five (125) aliens descended on a set of film as Extra Terrestrial beings. 40 had two noses, 30 had three legs, 20 had four ears, 10 had two noses, and three legs, 12 had 3 legs and four ears, 5 had two noses and four ears and 3 had all the unusual features. How many were there without any of these unusual features?

(a) 5

(b) 35

(c) 80

(d) None of these

Answer 1

Correct option is (d) None of these

Let A = set of aliens having two noses

B = set of aliens having three legs

C = set of aliens having four ears

n(A) = 40, n(B) = 30, n(C) = 20, n(A ∩ B) = 10, n(B ∩ C) = 12, n(C ∩ A) = 5, n(A ∩ B ∩ C) = 3

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − (n(A ∩ B) + n(B ∩ C) + n(C ∩ A)) + n(A ∩ B ∩ C)

n(A ∪ B ∪ C) = 40 + 30 + 20 − (10 + 12 + 5) + 3

n(A ∪ B ∪ C) = 40 + 30 + 20 − (10 + 12 + 5) + 3

n(A ∪ B ∪ C) = 66

Aliens having any of the deformities = 66

So, aliens without any deformities = 125 − 66 = 59