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(D) There are $3$ houses available and $3$ persons applying for them.Each person has $3$ choices for selecting a house.Since each person applies indep

Vedclass · Accepted Answer

$\frac{1}{9}$

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(D) There are $3$ houses available and $3$ persons applying for them.Each person has $3$ choices for selecting a house.Since each person applies independently,the total number of ways the $3$ persons can apply for the $3$ houses is $3 	imes 3 	imes 3 = 27$.For all $3$ persons to apply for the same house,they can either all choose the first house,all choose the second house,or all choose the third house.There are $3$ such favorable outcomes.Therefore,the probability that all $3$ persons apply for the same house is $\frac{3}{27} = \frac{1}{9}$.

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

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