in a certain examination,52 candidates offers biology, 60 offers history, 92 offers both biology and history,21 offers both biology and history, 22 mathematics and history. If 7 candidates offers all the three subjects
find
a.how many candidate who where there for the examination
b.how many candidate offer one subject only
c.how Many offers two subjects only
d.how many offers at least two subjects
Make up your mind:
92 offers both biology and history,21 offers both biology and history
To answer these questions, we can use the principle of inclusion-exclusion. Let's go step by step:
a. The total number of candidates who were there for the examination can be obtained by adding the number of candidates who took each subject individually and then subtracting the candidates who took multiple subjects to avoid counting them twice:
Total = Candidates taking Biology + Candidates taking History + Candidates taking Mathematics - Candidates taking both Biology and History - Candidates taking both Biology and Mathematics - Candidates taking both History and Mathematics + Candidates taking all three subjects.
Total = 52 (Biology) + 60 (History) + X (Mathematics) - 92 (both Biology and History) - 22 (both Biology and Mathematics) - 22 (both History and Mathematics) + 7 (all three subjects).
b. To find the number of candidates who offer only one subject, we need to add the candidates who took only Biology, only History, and only Mathematics. This can be calculated using the principle of inclusion-exclusion:
Candidates offering only one subject = Candidates taking Biology only + Candidates taking History only + Candidates taking Mathematics only.
Candidates offering only one subject = (52 - 92 - 7) + (60 - 92 - 7) + (X - 22 - 7).
c. To find the number of candidates who offer two subjects only, we need to add the candidates who took Biology and History only, Biology and Mathematics only, and History and Mathematics only:
Candidates offering two subjects only = Candidates taking Biology and History only + Candidates taking Biology and Mathematics only + Candidates taking History and Mathematics only.
Candidates offering two subjects only = (92 - 7) + (22 - 7) + (22 - 7).
d. To find the number of candidates who offer at least two subjects, we need to add the candidates who took both Biology and History, both Biology and Mathematics, both History and Mathematics, and all three subjects:
Candidates offering at least two subjects = Candidates taking both Biology and History + Candidates taking both Biology and Mathematics + Candidates taking both History and Mathematics + Candidates taking all three subjects.
Candidates offering at least two subjects = 92 + 22 + 22 + 7.
By plugging in the given values and solving the equations, we can find the answers to all four questions.
I've seen this incorrect wording before. The word "offer" is not used correctly here. You mean "take" or "took."
In a certain examination, 52 candidates took biology, 60 took history, 92 took both biology and history …
I'm hoping "Favour" will point this error out to his/her instructor so better textbooks will be chosen and better teaching will happen.