Advertisements
Advertisements
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 only carrom (Hint: Use Venn diagram)
Advertisements
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 only carrom
= 13 – x
= 13 – 5
= 8
APPEARS IN
RELATED QUESTIONS
State, whether the pair of sets, given below, are equal sets or equivalent sets:
{3, 5, 7} and {5, 3, 7}
In a class, all students take part in either music or drama or both. 25 students take part in music, 30 students take part in drama and 8 students take part in both music and drama. Find the total number of students in the class
In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who like both tea and coffee
In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who do not like tea
In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who do not like coffee
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)
In a class of 50 students, each one come to school by bus or by bicycle or on foot. 25 by bus, 20 by bicycle, 30 on foot and 10 students by all the three. Now how many students come to school exactly by two modes of transport?
If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C) = 10, then the value of x is
What is the cardinal number of an empty set?
If Set A has the unique elements {2, 3, 5}, which of the following correctly represents its cardinality?
