In a class of 40 students, each student plays at least one of the games. chess, carom and table tennis. Among the students, 18 play 20 play table tennis and 27 play carom, Further ,7 student play both chess and table tennis, 12 play both table tennis and carom and 4 play chess, carom and table tennis together. Find the number of students who play chess and carom but hot table tennis. (set)

Here, n(total) = 400

n(chess ) = 18, n(TT) = 20, n (carom) = 27.

n(chess & TT)=7, n(TT & carom)= 12 and n(Chess & Carom)=?

n(chess & TT & carom)=4

We have, 

n(total) = n(chess) + n(TT) + n (carom)-n(chess & TT) - n(TT & carom)- n(chess & carom) +

n(chess & TT & carom)

$\Rightarrow$ 40=18+20+27-7-12-n(chess & carom) + 4

n(chess & carom) = 50 - 40 = 10

So, total number of students who play both chess & carom is = 10.

But there are 4 students who play all the three games. So, the number of students who play chess and carom but not table tennis = 10-4=6. ans.