Question

Each student in a class of 35 plays at least one game among chess carrom and table tennis 22 play chess 21 play carrom 15play table tennis 10play 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 (ii) only chess (iii) only carrom use venn diagram

Answer 1

See the attachment .

Given :

Students who play chess = 22

Students who play carrom = 21

Students who play table tennis = 15

Students who play chess and table tennis = 10

Students who play carrom and table tennis = 8

Students who play all three games together = 6 .


Answer -

By using Venn diagram -


(1) Students who play chess and carrom but not table tennis = 5.

Explanation -

= 21 + 22 - 32 - 6

= 43 - 32 - 6

= 11 - 6

= 5



(2) Students who play only chess = 7

Explanation -

= 22 - 6 - 5 - 4

= 16 - 5 - 4

= 11 - 4

= 7 .



(3) Students who play only carrom = 8.

Explanation -

= 21 - 6 - 5 - 2

= 15 - 5 - 2

= 10 - 2

= 8.



Hence :

Answer : (1) = 5

Answer : (2) = 7

Answer : (3) = 8.