Each student in a class of 40 plays at least one indoor game chess, carrom and scrabble. 18
play chess, 20 play scrabble and 27 play carrom. 7 play chess and scrabble, 12 play scrabble
and carrom and 4 play chess, carrom and scrabble. Find the number of students who play (i)
chess and carrom. (ii) chess, carrom but not scrabble.
play chess, 20 play scrabble and 27 play carrom. 7 play chess and scrabble, 12 play scrabble
and carrom and 4 play chess, carrom and scrabble. Find the number of students who play (i)
chess and carrom. (ii) chess, carrom but not scrabble.
Answers & Comments
Answer:
10, 6
Step-by-step explanation:
Let A be the set of students who play chess
B be the set of students who play scrabble
C be the set of students who play carrom
Therefore, We are given n(A ∪ B ∪ C) = 40,
n(A) = 18, n(B) = 20 n(C) = 27,
n(A ∩ B) = 7, n(C ∩ B) = 12 n(A ∩ B ∩ C) = 4
We have
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)
Therefore, 40 = 18 + 20 + 27 - 7 - 12 - n(C ∩ A) + 4
40 = 69 – 19 - n(C ∩ A)
40 = 50 - n(C ∩ A) n(C ∩ A) = 50 - 40
n(C ∩ A) = 10
Therefore, Number of students who play chess and carrom are 10.
Also, number of students who play chess, carrom and not scrabble.
= n(C ∩ A) - n(A ∩ B ∩ C)
= 10 – 4
= 6