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This Question is not correct.
The Correct Question is below
3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8
Answer:
(A) 1/8
Explanation:
Let us assume that the total number of students at Social High is = 32
Therefore,
Since 3/8 of all students are in all 3 clubs,
The total number of students in the 3 clubs = (3÷8) × 32 = 12
Since 1/2 of all students are in Albanian club,
The total number of students in the Albanian club = (1÷2) × 32 = 16
Since 5/8 of all students are in Bardic club,
The total number of students in the Bardic club = (5÷8) × 32 = 20
Since 3/4 of all students are in Checkmate club,
The total number of students in the Checkmate club = (3÷4) × 32 = 24
From above information in the question, we know that zero(0) students are in none of the clubs.
Let X be given as the number of students in exactly two clubs, we can now use the equation:
Total number of Students at Social High = (Total number of students at Albanian club)+(Total number of students at Bardic club) + ( Total number of students at Checkmate club) - (Total number of Students in exactly two clubs) -2(Total number of students
in all the 3 clubs) + none
32 = 16 +20 +24 - X - 2(12) + 0
32 = 36+ 24 - X - 24
X = 36-32
X = 4
Therefore , the fraction of people in exactly two clubs = The total number of students in exactly two clubs/ The total number of students at Social High
= 4/32
= 1/8
The fraction of students in exactly two club is 1/8.
Answer:
1/8
Explanation:
Assuming there are say 40 students at Social high
No of students in all 3 clubs will be
3/8 x 40 = 15 students
The no of students in Albanian club will be
1/2 x 40 = 20 students
The number of students in Bardic club will be
5/8 x 40 = 25 students
The number of students in Checkmate club will be
3/4 x 40 = 30 students
Number of students in none of the club = 0
If we use B to denote the number of student in 2 clubs exactly, then using the knowledge of Sets and Venn Diagram we know that
Total number of students at social High = (Number of students at Albanian Club) + (Number of students at Bardic Club) + (Number of students at Checkmate Club) - (Number of Students in exactly two clubs) - 2 x (Total number of students in all 3 clubs) + (Number of student in none of the clubs)
40 = 20 + 25 + 30 - B - 2(15) + 0
B = 75 - 40 - 30
B = 5
Hence the fraction of students in exactly 2 clubs will be = number of students in exactly 2 clubs/Total number of students at Social High
= 5/80
= 1/8
