1. **State the problem:** We are given two finite sets $A$ and $B$ with $n(A) = 40$, $n(B) = 38$, and $n(A \cup B) = 60$. We need to find $n(A \cap B)$, the number of elements in the intersection of $A$ and $B$. 2. **Formula used:** The formula relating the sizes of two sets and their union and intersection is: $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$ 3. **Rearrange the formula to find $n(A \cap B)$:** $$n(A \cap B) = n(A) + n(B) - n(A \cup B)$$ 4. **Substitute the given values:** $$n(A \cap B) = 40 + 38 - 60$$ 5. **Calculate:** $$n(A \cap B) = 78 - 60 = 18$$ 6. **Conclusion:** The number of elements in the intersection of sets $A$ and $B$ is $18$.