Question

In a class with 42 students, 22 like blue and 27 like red. If 6 no like either colours. Find :- a) How many students like both red and blue b) How many students like red only c) How many students like blue only

Answer 1

27+22=49

so your question doesnt really make sense, can u re-word it and make sure your problem is correct

Answer 2

Answer:

a) 13 students like both red and blue.

b) 14 students like only red.

c) 9 students like only blue.

Solution:

Given that total students in class = 42

Number of students do not like any color = 6

So number of students do not like any or both color = 42 – 6= 36

Let A be the set representing students who like red,

So n(A) = 22, n(B) 27  

And $\mathrm{n}(\mathrm{AUB})=36$

a)Students who like both red and blue will be $n(A \cap B)$

$n(A \cup B)+(A \cap B)=n(A)+n(B)$

36+n(A \cap B)=22+27

$n(A \cap B)=49-36=13$

So 13 students like both red and blue.  

B)  Students who like only red:

Students who like only red=Number of students like red – Number of students like both red and blue

Students who like only red = n(B)-n(A) = 27 – 13 = 14

So 14 students like only red.

c)Students who like only blue:

Students who like only blue= Number of students like blue – Number of students like both red and blue

Students who like only blue= $n(A)-n(A \cap B)$ =22-13=9

So 9 students like only blue.