Final answer:
Using a Venn diagram approach, we determined that there are 1542 candidates in total at the examination center. There were 430 candidates who took both Mathematics and Physics.
Step-by-step explanation:
To determine the total number of candidates in the examination center using a Venn diagram, we must take into account the individual subject candidates as well as those who took multiple subjects. According to the given data, we have the following information:
- 960 candidates took Mathematics
- 780 candidates took Physics
- 572 candidates took Chemistry
- 300 candidates took both Mathematics and Physics
- 340 candidates took both Mathematics and Chemistry
- 260 candidates took both Physics and Chemistry
- 130 candidates took all three subjects
When we create the Venn diagram, we start by placing the 130 candidates who took all three subjects in the intersection of all three circles (representing Mathematics, Physics, and Chemistry). Then, we distribute the remaining numbers in the overlapping areas, making sure to subtract the ones who took all three subjects from those counted in the individual overlaps:
- Mathematics and Physics only: 300 - 130 = 170
- Mathematics and Chemistry only: 340 - 130 = 210
- Physics and Chemistry only: 260 - 130 = 130
Next, we calculate the numbers for those who took only one subject by subtracting the numbers in overlaps from the total number of candidates for each subject:
- Only Mathematics: 960 - (170 + 210 + 130) = 450
- Only Physics: 780 - (170 + 130 + 130) = 350
- Only Chemistry: 572 - (210 + 130 + 130) = 102
Finally, we add all the numbers to get the total number of candidates:
Total candidates = 450 (only Maths) + 350 (only Physics) + 102 (only Chemistry) + 170 (Maths & Physics) + 210 (Maths & Chemistry) + 130 (Physics & Chemistry) + 130 (all three) = 1542 candidates.
As for how many took Mathematics and Physics, it includes those who took both subjects and those who took all three: 300 + 130 = 430 candidates.