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 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
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}
State, whether the pair of sets, given below, are equal sets or equivalent sets:
{7, 7, 2, 1,2} and {1, 2, 7}
State, whether the pair of sets, given below, are equal sets or equivalent sets:
{8, 6, 10, 12} and {3, 2, 4, 6}
Write the cardinal number of the following set:
D= {3, 2, 2, 1, 3, 1, 2}
Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.
Find: A ∪ B AND n(A ∪ B)
State true or false for the following. Correct the wrong statement.
n(Φ) = 1
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 number of students who take part in only music
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Number of families buy only one newspaper
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
