To find $n(B \cup C)$, we need to determine the number of unique elements in the union of sets $B$ and $C$.

Given the sets:

• $B = \{ \text{Math, Drama, Chemistry, Psychology, History} \}$
• $C = \{ \text{English, French, Chemistry} \}$

First, let's list all the unique elements in $B \cup C$:

• Math
• Drama
• Chemistry (appears in both B and C, but we count it only once)
• Psychology
• History
• English
• French

So, the union of sets $B$ and $C$ is: $B \cup C = \{ \text{Math, Drama, Chemistry, Psychology, History, English, French} \}$

Next, we count the number of elements in this union: $n(B \cup C) = 7$

Thus, the number of elements in $B \cup C$ is $\boxed{7}$.

Would you like any details or have any questions? Here are some related questions that might interest you:

1. How do you find the intersection of two sets?
2. What is the difference between the union and the intersection of sets?
3. How can Venn diagrams help in understanding set operations?
4. What is the complement of a set?
5. How do you calculate the number of elements in the union of three sets?

Tip: When dealing with unions and intersections, always list out the elements to avoid counting duplicates!