Question

In a group of 120 students, 42 buy coke, 35 buy pepsi; 15 buy coke and pepsi; 8 buy coke
and Fanta; 4 buy fanta and pepsi but not coke ; 11 buy coke and pepsi but not Fanta. If
10 buy only Fanta, find how many buy a) Atleast 2 b) All 3 c) None of them.

Answer 1

Answer:

A) 23 Persons

B) 4 Persons

C) 48 Persons

Step-by-step explanation:

I'm not so sure about my calculation but let's do this...

Let @1 represents students who bought only Coke

@2 represents students who bought only Pepsi

@3 represents students who bought only Fanta

@4 represents students who bought Coke and Fanta but not Pepsi

@5 represents students who bought Coke and Pepsi but not Fanta

@6 represents students who bought Pepsi and Fanta but not Coke

@7 represents students who bought all 3 types

@8 represents students who bought nothing

From the question, we are given that

@1+@5+@4+@7 = 42

@2+@5+@6+@7 = 35

@5+@7=15

@4+@7=8

@6=4

@5=11

@3=10

##@1+@5=42-8=34

@1=34-11=23

@7=15-11=4

@2=35-4-11-4=16

@4=8-4=4

A) at least 2 = @4+@5+@6+@7 = 4 + 11 + 4 + 4 = 23 Persons

B) All = @7 = 4 Persons

C) None = 120 - (@1+@2+@3+...+@7) = 120 - (23+16+10+4+11+4+4) = 120 - 72 = 48 Persons