Question

Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play 

(i) chess and carrom but not table tennis 

(ii) only chess 

(iii) only carrom (Hint: Use Venn diagram)

Answer 1

A – Chess 

B – Carrom 

C – Table Tennis 

n(A) = 22 

n(B) = 21

n(C) = 15 

n(A ∩ C) = 10 

n(B ∩ C) = 8 

n(A ∩ B ∩ C) = 6

y = 22 – (x + 6 + 4) = 22 – (x + 10) 

= 22 – x – 10 

= 12 – x 

z = 21 – (x + 6 + 2) = 21 – (8 + x)

21 – 8 – x = 13 – x 

y + z + 3 + x + 2 + 4 + 6 = 35 

12 – x + 13 – x + 15 + x = 35 

40 – x = 35 

x = 40 – 35 = 5

(i) Number of students who play only chess and Carrom but not table tennis = 5

(ii) Number of students who play only chess = 12 – x = 12 – 5 = 7 

(iii) Number of students who play only carrom = 13 – x = 13 – 5 = 8