Question

in a class of 30 pupils 12 take chemistry 16 take physics and 18 take chemistry if all 30 students take atleast one subject and no one take all three then the no of pupils taking 2 subject is

please help... ​

Answer 1

Answer:

Solution: (1)

Total number of pupils = 30

Number of pupils taking Chemistry = n (C) = 12

Number of pupils taking Physics = n (P) = 16

Number of pupils taking History = n (H) = 18

n (C ∪ P ∪ H) = 30 and n (C ∩ P ∩ H) = 0

(C ∪ P ∪ H) = n (C) + n (P) + n (H) − n (C ∩ P) − n (P ∩ H) − n (H ∩ C) + n (C ∩ P ∩ H)

n (C ∩ P) + n (P ∩ H) + n (H ∩ C)

= (12 + 16 + 18) − 30

= 46 − 30

= 16

Answer 2

N = pupils who take needlework

P = pupils who take physics

C = pupils who take chemistry

n (N ∪ P ∪ H) = n (N) + n (P)+ n (H) − n (N ∩ P) − n (P ∩ H) − n (N ∩ H) + n (N ∩ P ∩ H)

n (N ∩ P) + n (P ∩ H) + n (N ∩ H) = 16