A household can watch news on any of the three networks $-\mathrm{ABC}$, $\mathrm{CBS}$, or $\mathrm{NBC}$. On a certain day, five households randomly and independently decide which channel to watch. Let $x$ be the number of households among these five that decide to watch news on $\mathrm{ABC}$. Is $x$ a discrete or a continuous random variable? Explain.