In examination 60 candidates offered mathematics, 80 offered English and 50 offered chemistry. If 20 offered mathematics and English, 15 English and chemistry, and 10 offered all three subjects, how many candidates sat the examination?
Well, it sounds like these candidates were ready to take on all the subjects like true superheroes of education! Let's break it down:
We know that 60 candidates offered mathematics, 80 offered English, and 50 offered chemistry.
Now, we also know that 20 candidates offered mathematics and English, 15 offered English and chemistry, and 10 offered all three subjects.
To figure out the total number of candidates who sat the examination, we need to sum up the number of candidates who offered each subject.
If we add up all the candidates who offered each subject individually, we get:
Mathematics candidates + English candidates + Chemistry candidates
So, the total number of candidates would be:
60 + 80 + 50 = 190
However, we need to remember that we counted some students more than once. That's because there were candidates who took more than one subject.
To adjust for that, we need to subtract the candidates who took multiple subjects. So let's do that.
We know that there were 10 candidates who took all three subjects, so we subtract that from our total:
190 - 10 = 180
Therefore, there were a total of 180 candidates who sat the examination, eager to tackle these subjects head-on!
To find the total number of candidates who sat the examination, we need to add the number of candidates who offered each subject individually. Let's break down the information given:
- Number of candidates who offered mathematics = 60
- Number of candidates who offered English = 80
- Number of candidates who offered chemistry = 50
Now, let's consider the candidates who offered multiple subjects:
- Number of candidates who offered both mathematics and English = 20
- Number of candidates who offered both English and chemistry = 15
- Number of candidates who offered all three subjects = 10
To calculate the total number of candidates who sat the examination, we can add these numbers together:
60 (mathematics) + 80 (English) + 50 (chemistry) - 20 (mathematics and English) - 15 (English and chemistry) + 10 (all three subjects) = 165
Therefore, the total number of candidates who sat the examination is 165.
To find out the total number of candidates who sat the examination, we need to add the number of candidates who offered each subject separately and then subtract the candidates who offered multiple subjects multiple times.
Given information:
- Number of candidates offered mathematics (M) = 60
- Number of candidates offered English (E) = 80
- Number of candidates offered chemistry (C) = 50
- Number of candidates who offered mathematics and English (M&E) = 20
- Number of candidates who offered English and chemistry (E&C) = 15
- Number of candidates who offered all three subjects (M&E&C) = 10
To find the total number of candidates who sat the examination, we will apply the principle of inclusion-exclusion.
Step 1: Add the number of candidates who offered each subject separately:
M + E + C = 60 + 80 + 50 = 190
Step 2: Subtract the candidates who offered multiple subjects multiple times:
(M&E) + (E&C) + (M&E&C)
Since the candidates who offered all three subjects (M&E&C) are already included in both (M&E) and (E&C), we only need to subtract them once.
Subtracting (M&E) + (E&C) + (M&E&C) = 20 + 15 + 10 = 45 from the total, we get:
Total candidates = M + E + C - (M&E) - (E&C) - (M&E&C)
= 190 - 45
= 145
Therefore, the total number of candidates who sat the examination is 145.