Answer:
Step-by-step explanation:
To find the total number of candidates for the examination, you can use the principle of inclusion-exclusion. This principle helps you account for the overlaps between different sets.
Let's denote:
- \(M\) as the set of candidates who offered Mathematics,
- \(E\) as the set of candidates who offered English,
- \(F\) as the set of candidates who offered French.
The total number of candidates (\(N\)) can be expressed as:
\[ N = |M \cup E \cup F| \]
Using the inclusion-exclusion principle, this is given by:
\[ N = |M| + |E| + |F| - |M \cap E| - |M \cap F| - |E \cap F| + |M \cap E \cap F| \]
Now, let's plug in the given values:
\[ N = 72 + 64 + 62 - 18 - 24 - 20 + 8 \]
Calculate each term:
\[ N = 142 - 62 \]
So, the total number of candidates for the examination is \(80\).
