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25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is
Correct answer is '3'. Can you explain this answer?
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25 persons are in a room. 15 of them play hockey, 17 of them play foot...
number of player=25,
player who play either football or hockey=17+15,
play both hockey and football=10.
then players who play=32-10=22
then players who do not play =25-22=3
Most Upvoted Answer
25 persons are in a room. 15 of them play hockey, 17 of them play foot...
Given information:
● Total number of persons in the room = 25
● Number of persons playing hockey = 15
● Number of persons playing football = 17
● Number of persons playing both hockey and football = 10
To find:
Number of persons playing neither hockey nor football
Solution:
We can use the principle of inclusion and exclusion to find the number of persons playing neither hockey nor football. This principle states that:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
where n(A) denotes the number of elements in set A.
Let's apply this principle to the given information:
● Let A be the set of persons playing hockey.
● Let B be the set of persons playing football.
● Let C be the set of persons playing both hockey and football.
● Let S be the set of all persons in the room.
We want to find the number of persons in the set S - (A ∪ B), which represents the set of persons who are not playing hockey or football.
n(S - (A ∪ B)) = n(S) - n(A ∪ B)
= n(S) - (n(A) + n(B) - n(A ∩ B))
= 25 - (15 + 17 - 10)
= 3
Therefore, the number of persons playing neither hockey nor football is 3.
Conclusion:
3 persons are playing neither hockey nor football.
● Total number of persons in the room = 25
● Number of persons playing hockey = 15
● Number of persons playing football = 17
● Number of persons playing both hockey and football = 10
To find:
Number of persons playing neither hockey nor football
Solution:
We can use the principle of inclusion and exclusion to find the number of persons playing neither hockey nor football. This principle states that:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
where n(A) denotes the number of elements in set A.
Let's apply this principle to the given information:
● Let A be the set of persons playing hockey.
● Let B be the set of persons playing football.
● Let C be the set of persons playing both hockey and football.
● Let S be the set of all persons in the room.
We want to find the number of persons in the set S - (A ∪ B), which represents the set of persons who are not playing hockey or football.
n(S - (A ∪ B)) = n(S) - n(A ∪ B)
= n(S) - (n(A) + n(B) - n(A ∩ B))
= 25 - (15 + 17 - 10)
= 3
Therefore, the number of persons playing neither hockey nor football is 3.
Conclusion:
3 persons are playing neither hockey nor football.
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25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football isCorrect answer is '3'. Can you explain this answer?
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25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football isCorrect answer is '3'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football isCorrect answer is '3'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football isCorrect answer is '3'. Can you explain this answer?.
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