Here's a table view of the overlapping sets:
Attachment:
overlap_calceng.png [ 41.98 KiB | Viewed 599 times ]
First, we know the total is 2400.
Then, given that they must take at least one of the subjects, we know the number of students who do
not take calculus
and do
not take english is 0. This fills the "middle" square.
Next, half of the total number of students take calculus. So we know 1200 take calculus and 1200 do not. This fills the "bottom" row.
Of the 1200 who take calculus, a third of those students also take english. So, 400 students take english
and calculus. This leaves 800 students who take calculus
and do
not take english. This fills the "left" column.