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 three apply for same house is

Options

A. `(7)/(9)`
B. `(8)/(9)`
C. `(1)/(9)`
D. `(2)/(9)`

Answer

C

Explanation

Each persons can apply for any house. Therefore, total number of ways in which three persons can apply for three houses in `3xx3xx3=27` ways.
Since three persons can apply for house 2 or house 3.
So, three persons can apply for the same house in 3 ways.
`therefore` Favourable number of ways =3.
So, required probability `=(3)/(27)=(1)/(9)`