Question

In a meeting it was found that 25 people preferred to have coffee, 21 people preferred biscuits and 20 people cake. If 9 people preferred coffee and biscuits, 10 people opted for biscuits and cake, 11 people liked to have coffee and cake and 7 people chose all the three. Find: (i) the number people in the meeting. (ii) how many preferred to take coffee only?​

Answer 1

Step-by-step explanation:

the total no.of people in the meeting is 43

25+21+20-9-10-11+7=43

No. of people who preferred coffee only= 12

Answer 2

no. of coffee drinkers =n(A)=25 people

no. of biscuit eater=n(B)=21 people

no. of cake eater= n(C)=20 people

n(A n B)=9

n(B n C)=10

n(A n C)=11

n(A n B n C)=7

n(A U B U C)=n(A)+n(B)+n(C)-n(A n B)-n(B n C)-n(A n C)+n(A n B n C )

=25+21+20-9-10-11+7

=66-30+7

=36+7

n( A U B U C)=43

total number of people's =43

people who prefers coffee only=

n(A)-n(A n B)-n(A n C)+n(A n B n C)

=25-9-11+7

=25-20+7

=5+7

=12