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 chess and carrom but not table tennis (**Hint:** Use Venn diagram)

#### Solution

Let A, B and C represent students play chess, carrom and table tennis.

n(A) = 22, n(B) = 21, n(C) = 15

n(A ∩ C) = 10, n(B ∩ C) = 8, n(A ∩ B ∩ C) = 6

Let “x” represent student play chess and carrom but not table tennis.

Let us represent the data in Venn diagram.

From the Venn diagram we get,

Number of students play atleast one game = 35

12 – x + x + 13 – x + 2 + 6 + 4 + 3 = 35

40 – 35 = x

5 = x

Number of students who play chess and carrom but not table tennis = 5