In a certain examination, 52 candidates offered Biology, 60 candidates offered History and 96 offered Mathemathics, if 21 candidates offered biology and History, 22 candidates offered Biology and mathematics, 16 candidates offered History and methematics, 17 candidates offered all the three subjects. Draw a venn diagram. 1. how many candidates sat for the examination, 2. How many candidates offered onlybone subject 3. how many candidates offered two subjects
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In a certain examination, 52 candidates offered biology, 60 candidates offered history and 96 offered mathematics . If 21 candidates offered biplogy and biology and history, 22 candidates offered biology and mathetics, 16 candidates offered history and mathematics, 17 candidates offered all the three subject. Draw a venn diagram to illustrate these information and, how many candidates sat for the examinaton, how many candidates offered only one subject, how many candidates offered two subject?
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To solve this problem, we can use Venn diagrams.
1. To determine the total number of candidates who sat for the examination, we need to add up the number of candidates who offered each subject: Biology (52), History (60), and Mathematics (96). However, when we do this, we would count the candidates who offered more than one subject multiple times. So, to avoid double-counting, we need to subtract the candidates who offered two or more subjects.
To find the candidates who offered two or more subjects, we can add up the numbers of candidates who offered two subjects (Biology and History = 21, Biology and Mathematics = 22, History and Mathematics = 16), and subtract the number of candidates who offered all three subjects (17):
Total number of candidates who sat for the examination = Biology + History + Mathematics - (Biology and History) - (Biology and Mathematics) - (History and Mathematics) + (Biology, History, and Mathematics)
= 52 + 60 + 96 - 21 - 22 - 16 + 17
= 166
Therefore, there were a total of 166 candidates who sat for the examination.
2. To find the number of candidates who offered only one subject, we can add up the candidates who offered each subject separately (Biology, History, and Mathematics), and then subtract the candidates who offered two or more subjects (Biology and History, Biology and Mathematics, History and Mathematics). We also need to subtract the candidates who offered all three subjects (since they are not offering only one subject):
Candidates offering only one subject = (Biology + History + Mathematics) - (Biology and History) - (Biology and Mathematics) - (History and Mathematics) - (Biology, History, and Mathematics)
= 52 + 60 + 96 - 21 - 22 - 16 - 17
= 132
Therefore, 132 candidates offered only one subject.
3. To find the number of candidates who offered two subjects, we need to add up the candidates who offered two subjects at a time (Biology and History, Biology and Mathematics, History and Mathematics), and subtract the candidates who offered all three subjects (since they are not offering only two subjects):
Candidates offering two subjects = (Biology and History) + (Biology and Mathematics) + (History and Mathematics) - (Biology, History, and Mathematics)
= 21 + 22 + 16 - 17
= 42
So, there were 42 candidates who offered two subjects.
Finally, to represent this information in a Venn diagram, we would have three overlapping circles: one for Biology, one for History, and one for Mathematics. The region where all three circles overlap will represent the candidates who offered all three subjects (17 in this case). The regions where each pair of circles overlap will show the candidates who offered two subjects, and the regions outside of any overlap will show the candidates who offered only one subject.