Question

each students 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 a)chess and carrom but not table tennis;b)only chess ;c)only carrom.

Answer 1

Answer:

n(Chess)=22=C

n (Carrom)=21=CA

n (Table Tennis)= 15=T

n (C ∩ T )=10

n ( C A ∩ T)= 8

n ( C ∩ C A ∩ T )=6

⇒n (C ∪ CA ∪ T)=n(C) +n (C A) +n (T)-n (C ∩ CA) -n(CA ∩ T)-n(T ∩ C)+n ( C ∩ C A ∩ T )

⇒35=22+21+15-n (C ∩ CA)-8-10+6

⇒35 = 58-12-n (C ∩ CA)

⇒n (C ∩ CA)=46-35

⇒n (C ∩ CA)=11

Number of students who play chess and Carrom but not table tennis

      = n (C ∩ CA)- n ( C ∩ C A ∩ T )

        =11 -6

        =5

Number of students who play chess only

         = n (C) -n(C∩T)-n(C∩CA)+n ( C ∩ C A ∩ T )

         = 22 - 10 - 11 + 6

         =28 -21

          =7

Number of students who play Carrom only

         = n (CA) -n(CA∩T)-n(C∩CA)+n ( C ∩ C A ∩ T )

         = 21 - 8 -11+ 6

          =27 -19

          =8