Question

I don't know why I can't seem to get the answer to this one. Can anyone help?
In a school of 458 students, 82 students are in the band, 197 students are on sports teams and 36 students participate in both activities. How many students in the school are not enrolled in either sports teams or band?

Answer 1

a venn might help; what have you tried?

Answer 2

n(T or B) = nT + nB - n(T and B)

458 - n(T or B)

Answer 3

a.
261
b.
179
c.
422
d.
215
based off of these answers I haven't been able to figure it out.

Answer 4

dont base it off the answers options then ....

Answer 5

Those are the only options I have as a final answer.

Answer 6

if we count all the elements of the left set we get: a+b
if we count all the elements of the right set we get: b+c

if we count all the elements of both sets we get: a+b+b+c .... notice that this is heavey by a "b"

Answer 7

the value of A or B is therefore: A + B, minus the common parts, AnB

Answer 8

82 + 197 is 36 heavy ... its counted twice

82 + 197 - 36 accounts for all the student taking band and/or team sports

458 - (82 + 197 - 36) is everyone else