In a survey of 100 students of a college it was found that 49 liked watching football, 53 likwatching hockey and 62 liked watching basket ball. 27 liked watching football and hockeboth, 29 liked watching basket ball and hockey both, 28 liked watching football and baskıball both. 5 liked watching none.Based on the above informationHow many students like watching all the games. a-95 b-15 c-5 d-80
Answers
Answer:
A-95
Step-by-step explanation:
a-95 because 5 students didn't like any games
The number of students who watch all the three sports is 15 students.
- Given:
Total number of students (U) = 100
Number of students who do not watch anything = 5
Number of students who watch football (A) = 49
Number of students who watch hockey (B) = 53
Number of students who watch basketball (C) = 62
Number of students who watch football and hockey (A∩B)= 27
Number of students who watch basketball and hockey (B∩C) = 29
Number of students who watch football and basketball (A∩C) = 28
- Now,
n(A∪B) = n(∪) - people who have do not watch anything
n(A∪B) = 100 - 5 = 95
- Now, the formula using sets is
n(A∪B∪C) = n(A) + n(B) + n(C) -n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
- Now, we have to find the number of students who watch all the three that is A∩B∩C.
Substituting the values in the formula , we get
95 = 49 + 53 + 62 - 27 - 28 -29 + n(A∩B∩C)
95 = 164 - 84 + n(A∩B∩C)
95 = 80 + n(A∩B∩C)
n(A∩B∩C) = 95 - 80
n(A∩B∩C) = 15
- 15 students watch all the three sports.