Question:
How many whole numbers between 99 and 999 contain exactly one 0?

Answer:
Numbers with exactly one zero have the form $\_ 0 \_$ or $\_ \_ 0$, where the blanks are not zeros.  There are $(9\cdot1\cdot9)+(9\cdot9\cdot1) = 81+81 = \boxed{162}$ such numbers.