Question

A school has 39 vacancies teacher, out of which 22 are for English language, 21 for mathematics and 17 for fine art. Of these vacancies 11 are for both English language and mathematics, 8 for both mathematics and fine art and 7 for English language and fine art. Using Venn diagram, find the number of teacher who must be able to teach all the three subjects​

Answer 1

Given :  A school has 39 vacancies teacher, out of which 22 are for English language, 21 for mathematics and 17 for fine art. Of these vacancies 11 are for both English language and mathematics, 8 for both mathematics and fine art and 7 for English language and fine art

To find  : find the number of teacher who must be able to teach all the three subjects​

Solution:

Total Vacancies = 39

English  E = 22

Mathematics M = 21

Fine Art  A = 17

English & Mathematics  E ∩ M  = 11

Mathematics and fine art M ∩ A  = 8

English and fine art E ∩ A  = 7

All subjects  = E ∩ M ∩ A

None = 0 ( in this case )

Total = E + M + A - E ∩ M - M ∩ A  - E ∩ A + E ∩ M ∩ A  + None

=> 39 = 22 + 21 + 17 - 11 - 8 - 7  + E ∩ M ∩ A  + 0

=> E ∩ M ∩ A = 5

number of teacher who must be able to teach all the three subjects​ = 5

Learn More:

125, 100 and 145 students appeared at post graduate examination ...

https://brainly.in/question/13477941

Which of venn diagrams best represent the relation between square ...

https://brainly.in/question/12163163