Answer:
The number of students in the key club is 490
Step-by-step explanation:
The given parameters are;
The number of student in the school = 1000
The total number of student in the debate club = 310
The total number of student in the student council = 650
The total number of student who are in debate and student council = 170
The total number of student who are in both debate and the key club = 150
The total number of student who are in both student council and the key club = 180
The number of students who are in all three clubs = 50
Therefore, we have;
Let A represent the number of students in the debate club
Let B represent the number of students in the student council
Let C represent the number of students in the key club
We have;
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C)
Where;
n(A∪B∪C) = 1000
n(A) = 310
n(B) = 650
n(A∩B) = 170
n(B∩C) = 180
n(C∩A) = 150
n(A∩B∩C) = 50
Therefore;
n(C) = n(A∪B∪C) - (n(A) + n(B) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C))
Substituting the values gives;
n(C) = 1000 - (310 + 650 - 170 - 180 - 150 + 50) = 490
The number of students in the key club, n(C) = 490.
