Question

Out of 40 students in a class , 16 study English , 22 Accountancy and 26 economics , 5 study English and economics , 14 study accountancy and economics , 2 study all three subject . If each student studies atleast one of the three subjects , find the number of students who study
1: English and Accountancy
2: English , Accountancy but not economics

Answer 1

Step-by-step explanation:

• this can be easily solved by venn diagram

Answer 2

1. The number of students study English and Accountancy is 7.

2. The number of students study English , Accountancy but not economics is 5.

Explanation:

Let E = Number of students study English .

A = Number of students study Accountancy .

C = Number of students study Economics.

Since each student studies atleast one of the three subjects

As per given , we have

E∪A∪C = 40 ,

E= 16  , A= 22  , C= 26

E∩C= 5 , A∩ C= 14

E∩A∩C = 2

Using formula of sets:

E∪A∪C =  E + A + C - E∩A - E∩C - A∩ C + E∩A∩C

i.e. E∩A= E+A+C-E∩C- A∩ C+E∩A∩C-E∪A∪C

Put values ,

E∩A= 16+22+26-5-14+2-40 =7

Therefore , the number of students who study English and Accountancy =7

2. The number of students study English , Accountancy but not economics= E∩A -E∩A∩C = 7-2=5

∴ The number of students study English , Accountancy but not economics is 5.

# Learn more :

Out of atleast 20 members in a family, 11 like to take tea and 14 like coffee. Assume that that each one likes at least one of two drinks. How many like only tea and not coffee?

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