In a group of 500 people 350 people can speak E... - JAMB Mathematics 2023 Question

Let \(F\) be the set of people who can speak French, and \(E\) be the set of people who can speak English.

Given that:

\[ n(F) = 400 \]

\[ n(E) = 350 \]

\[ n(F \cup E) = 500 \]

We want to find \(n(F \cap E)\) (the number of people who can speak both languages).

The inclusion-exclusion principle states:

\[ n(F \cup E) = n(F) + n(E) - n(F \cap E) \]

Substitute the given values:

\[ 500 = 400 + 350 - n(F \cap E) \]

Solve for \(n(F \cap E)\):

\[ n(F \cap E) = 750 - 500 = 250 \]

Therefore, \(250\) people can speak both languages.

So, the correct answer is 250.