JEE MAIN - Mathematics (2005 - No. 28)
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 :
$${2 \over 9}$$
$${1 \over 9}$$
$${8 \over 9}$$
$${7 \over 9}$$
Explanation
Person 1st has three options to apply.
Similarly, person 2nd has three options t apply
and person 3rd has three options to apply.
Total cases = 33
Now, favourable cases = 3 (An either all has applied for house 1 or 2 or 3)
So, probability $$ = {3 \over {{3^3}}} = {1 \over 9}$$.
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