Question

2. At a party, there are 10 people with white sh people have black shoes and white shirts. 3 people have black The total number of people with white or r people have black shoes? irts and 8 people with red shirts.4 shoes and red shirts. ed shirts or black shoes is 21. How many a. 1 b. 2 С. 3 d. 4 e.s g. 7 h. 8 i. 9 j. 10

Answer 1

Let W= people with white shirts

R= people with red shirts

B= people with black shoes and n(x) = no of peoples,x=W,R,B

So,n(W)=10, n(R)=8, $n(R\cap W)=0,n(B\cap W)=4,n(B\cap R)=3$ as one can not use red and white shirts simultaneously so intersection of R and W is 0. And also $n(R\cap W \cap B)= 0$ .

And $n(R\cup W\cup B)= 21$

So,$n(R)+n(B)+n(W)-n(R\cap B)- n(R\cap W)- n(B\cap W)+n(R\cap B\cap W) =21$

$8+n(B)+10-3- 0- 4+0=21$

$n(B)=10$

Hence 10 people has black shoes