# 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 :

$\begin {array} {1 1} (A)\;\large\frac{8}{9} & \quad (B)\;\large\frac{7}{9} \\ (C)\;\large\frac{2}{9} & \quad (D)\;\large\frac{1}{9} \end {array}$

For a particular house being selected, probability = $\large\frac{1}{3}$
Probability all the persons apply for the same house = $\bigg( \large\frac{1}{3} \times \large\frac{1}{3} \times \large\frac{1}{3} \bigg) 3$
$= \large\frac{1}{27} \times 3$
$= \large\frac{1}{9}$
Ans : (D)