16/40 students take math21/40 students take chemistry18/40 students take physics9/40 take math and chemistry5/40 take math and physics3/40 take all three subjects This doesn't add up because this would imply that 9+5+3 students take math, but not only math; however, that equals 17...
16/40 students take math
21/40 students take chemistry
18/40 students take physics
9/40 take math and chemistry
5/40 take math and physics
3/40 take all three subjects
This doesn't add up because this would imply that 9+5+3 students take math, but not only math; however, that equals 17 students?
Edit: because I assumed that the three groups were mutually exclusive. ie. the 3 taking all three subjects were not accounted for in the math/chemisty or math/physics group.
If they are not mutually exclusive then it would be be 16 - (9+5-3) = 5 students taking math only.
To solve for the number of students taking physics and chemisty sum the number of students taking physics and the num of students taking chemistry first: 21+18 = 39
Subtract from it all other possible combinations: 39 - 5 (math only) - 9 (math and chemistry) - 5 (math and physics) - 7 (physics only) - 8 (chemistry only) + 3 (all three) = 8