Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
\[ \begin{aligned} \text{No. of houses} &= 3 = \text{No. of favourable cases} \\ \text{No. of applicants} &= 3 \\ \text{Total number of events} &= 3^3 \quad \text{(because each candidate can apply in 3 ways)} \\ \text{Required probability} &= \frac{3}{3^3} = \frac{1}{9} \end{aligned} \]
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