In a cyclic group of order $n$, the number of elements that have order $k$ is given by $\phi(k)$, where $\phi(k)$ is the Euler's totient function evaluated at $k$.
So, the correct number of elements in a cyclic group of order $n$ that have order $k$ is $\phi(k)$.
In the context of the specific question, we are dealing with the cyclic group $\mathbb{Z}_{50}$ of order 50. We want to find elements of order 10, so we need to calculate $\phi(10)$.
Using Euler's totient function, $\phi(10) = 4$.
Therefore, the correct number of elements of order 10 in $\mathbb{Z}_{50}$ is 4.
The correct answer is:
(B) 4.