In a class 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible 5 opted Chemistry course. Then the number of student who did not opt for any of the three courses is :
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Sol. n(P) = 
= 46
n(c) = 
= 28
n(M) = 
= 70
n (P ∪ C ∪ M) = n(P) + n(c) + n(M) – n(P ∩ C) – n(C ∩ M) – n(M ∩ P) + n (P ∩ M ∩ C)
= 46 + 28 + 70 – 
– 
– 
+ 
= 144 – 9 – 14 – 23 + 4
= 102
so required number of student = 140 – 102 = 38
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